An experimental take
Exclusive implies that you have measured the energy and momenta of all the products (well, with an exception I'll discuss below). Inclusive means that you may have left some of the products unmeasured.
This applies to scattering processes as well as decays.
Some things to note:
- Exclusive measurements allow you to nail down one, well defined physics process, while inclusive measurements may tell you about a collection of processes
- It is generally difficult to measure neutral particles
- If there are more than a couple of products it begins to require a lot of instrumentation to reliably collect them all and (crucially) to know how well you have done so
In the process you are asking about the neutrino is necessarily unobserved rendering the measurement inclusive, further an $X$ in the final state is often used to indicate unmeasured and unspecified stuff (i.e. it means the measurement is inclusive by design).
Here unspecified includes case in high acceptance instruments where you consider all events with the specified products: those for which we know $X$ is empty, those for which $X$ is non-empty and well characterized, and those for which $X$ is ill-characterized.
Theoretical view
I'm less sure of how theorist use these terms, but I believe there is a parallel. Something like: exclusive means one and only one process, while inclusive means all processes that include the specified products.
Convergence of theory and experiment
Of course, we haven't really learned anything until we get theory and experiment together, which is sometimes traumatic for both communities. Still exclusive measurements and calculations are clearly talking about the same thing, and inclusivity can be made to agree with some care in building the experiment and assembling the theoretical results.
Experimenters cheating on exclusivity
Sometimes in nuclear physics we talk about scattering measurements as exclusive when there is an unmeasured, heavy, recoiling nucleus involved. The assumption being that that it carries a small fraction of the total energy and momentum involved and can be neglected, though there is some risk from this if the nucleus is left in a highly excited state.
In particular my dissertation project was on $A(e,e'p)$ reaction (elastic scattering of protons out of a stationary nuclear target where the beam was characterized and both the proton and outgoing electron were observed), and we assumed that the remnant nucleus was left largely undisturbed and recoiling with a momentum opposite the Fermi motion of the target proton.
A constitutive law is generally an algebraic relation which tells you the coefficients of a differential equation, while the governing equations are the differential equations themselves.
For example, if I have a metal piston on top of a gas, I can write down the equation of motion for the piston
$$m \ddot X - PA = 0$$
Where P is the pressure in the gas and A is the area of the piston. Without knowing how the pressure depends on the piston position, this is not a closed equation--- it refers to an undetermined quantity, the pressure. But the ideal gas law, that the pressure $P=C/(V-AX)$ where C,V are constants, determines the pressure in terms of X, and gives
$$ m \ddot X -{ AC\over (V - AX)} =0$$
Now the equation is closed--- it tells you the future behavior of X knowing X alone. The ideal gas law is the constitutive relation in this case, while the differential equation is the governing equation.
Constitutive equations are algebraic, governing equations are differential.
Best Answer
The reference document for metrological terms is the International Vocabulary of Metrology (VIM). Definitions there are carefully crafted, but frequently they might seem a bit obscure to non metrologists and further remarks might be needed.
For what concerns realization and reproduction (representation is also found in the literature for reproduction), their meaning is found under the term measurement standard:
In particular, the related notes 1 and 3 say:
Therefore, the terms realization and reproduction denote an object or an experiment with specific properties.
To illustrate the difference between a strict realization and a reproduction, let's take the example of a specific quantity, the unit ohm (note that a unit is a quantity, albeit a specially chosen one).
First, we have to define what this quantity is: this can be done in words, possibly with the help of mathematical relationships involving other quantities, and by adding specifications on influence quantities.
The ohm in the SI is defined as follows [CIPM, 1946: Resolution 2]:
So far, so good, or, at least, it seems. Actually we are a bit stuck because we can realize the ampere and the volt respectively through current and voltage balances, but the reproducibility of the ohm realized in this way would be low, roughly at the $10^{-6}$ level. And the procedure would be rather complex. We are saved in 1956 by Thompson and Lampard who discovered a new theorem in electrostatics [1], which is the electrostatic dual of the van der Pauw theorem [2,3]. This theorem essentially says that you can build a standard of capacitance (that is, realize the farad or one of its submultiples), whose capacitance can be accurately calculated (something you cannot do with a parallel plate capacitor, for instance). If we have a standard of capacitance, through the relationships $Y = \mathrm{j}\omega C$ and $Z = 1/Y$, we have the standards of admittance and impedance, that is, we have the siemens and the ohm, however in the AC regime.
Thus, the strict SI realization of the ohm, as standard of resistance, is roughly the following:
Once you have all the experiments working (after many years), the realization of the ohm through the above chain of experiments can take more than one month, but the most important issue is that the reproducibility of the ohm realized in this way, though better than that obtainable through the realizations of the volt and the ampere, is just at the $10^{-7}$-$10^{-8}$ level.
Then it arrives the quantum Hall effect (QHE). A QHE element under conditions of low temperature and high magnetic field, realizes a four terminal resistance (or transresistance) with resistance value $R_\mathrm{H} = R_\mathrm{K}/i$, where $R_\mathrm{K}$ is a constant, the von Klitzing constant, and $i$ is an integer, called plateau index (typically we use the plateau corresponding to $i=2$). By the end of the 1980s it was clear that QHE elements could provide resistance standards with much better reproducibility than the other methods described above: at the time, of the order of $10^{-8}$-$10^{-9}$; nowadays, of the order of $10^{-10}$-$10^{-11}$ (two-three order of magnitudes better than that obtainable with a calculable capacitor). It turns out, also, that the von Klitzing constant is linked to two fundamental constants, the Planck constant and the elementary charge, $R_\mathrm{K} = h/e^2$.
The situation in the late 1980s is thus the following:
The first two points suggest the adoption of a conventional unit of resistance, by defining a conventional value of the von Klitzing constant [CIPM, 1988: Recommendation 2]. This conventional value of the von Klitzing constant is denoted by $R_{\mathrm{K}-90}$ (because it was adopted in 1990) and has value
$$R_\mathrm{K-90} = 25\,812.807\,\Omega\quad \text{(exact)}.$$
The conventional unit of resistance is the $\mathit{\Omega}_{90}$, defined as 1
$$\mathit{\Omega}_{90} = \frac{R_\mathrm{K}}{\{R_\mathrm{K-90}\}} = \frac{R_\mathrm{K}}{25\,812.807}.$$
At present, virtually all national resistance scales are traceable to this conventional unit.
It is now worth pointing out that the quantity $\mathit{\Omega}_{90}$ has no links to the SI ohm: it's close to (the relative discrepancy is of the order of $10^{-8}$), but quite not the same thing. Thus, the $\mathit{\Omega}_{90}$ is called a reproduction (or a representation) of the ohm, because it realizes somehow the ohm, but not according to its definition.
At present, this is not the only reproduced unit: the volt is currently reproduced by means of the Josephson effect through a conventional value of the Josephson constant, and the thermodynamic temperature scale is reproduced through two conventional temperature scales, the International Temperature Scale of 1990 (ITS-90) and the Provisional Low Temperature Scale of 2000 (PLTS-2000).
Instead, with the forthcoming revision of the International System of Units, the so called "new SI", the quantum Hall effect and the Josephson effect will really provide SI realizations of the ohm and the volt (see this draft of the mise en pratique of the electrical units).
Finally, for what concerns the term implementation, as far as I know, it has no specific technical meaning within the community of metrologists, and it is used in the common English meaning (whereas realization has a somehow different connotation). Thus, for instance, we can speak of two different implementations of a quantum Hall resistance experiment (because some details might be different).
Notes
1 A note on notation: the quantity $\mathit{\Omega}_{90}$ is typeset in italics because it's not an SI unit; braces denote the numerical value of a quantity, according to the notation $Q = \{Q\}[Q]$ [4,5, and this question].
References
[1] A. M. Thompson and D. G. Lampard (1956), "A New Theorem in Electrostatics and its Application to Calculable Standards of Capacitance", Nature, 177, 888.
[2] L.J. van der Pauw (1958), "A method of measuring specific resistivity and Hall effect of discs of arbitrary shape", Philips Research Reports, 13, 1–9.
[3] L.J. van der Pauw (1958), "A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape", Philips Technical Review, 20, 220–224.
[4] E. R. Cohen et al. (2008), Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge [Online]
[5] E R Cohen and P. Giacomo (1987), Symbols, Units, Nomenclature and Fundamental Constants in Physics, IUPAP SUNAMCO Red Book, 1987 revision, IUPAP & SUNAMCO, Netherlands [Online]