Notice:
Perturbative string theory is defined to be the asymptotic perturbation series which are obtained by summing correlators/n-point functions of a 2d superconformal field theory of central charge -15 over all genera and moduli of (punctured) Riemann surfaces.
Perturbative quantum field theory is defined to be the asymptotic perturbation series which are obtained by applying the Feynman rules to a local Lagrangian -- which equivalently, by worldline formalism, means: obtained by summing the correlators/n-point functions of 1d field theories (of particles) over all loop orders of Feynman graphs.
So the two are different. But for any perturbation series one can ask if there is a local non-renormlizable Lagrangian such that its Feynman-rules reproduce the given perturbation series at sufficiently low energy. If so, one says this Lagrangian is the effective field theory of the theory defined by the original perturbation series (which, if renormalized, is conversely then a "UV-completion" of the given effective field theory).
Now one can ask which effective quantum field theories arise this way as approximations to string perturbation series. It turns out that only rather special ones do. For instance those that arise all look like anomaly-free Einstein-Yang-Mills-Dirac theory (consistent quantum gravity plus gauge fields plus minimally-coupled fermions). Not like $\phi^4$, not like the Ising model, etc.
(Sometimes these days it is forgotten that QFT is much more general than the gauge theory plus gravity plus fermions that is seen in what is just the standard model. QFT alone has no reason to single out gauge theories coupled to gravity and spinors in the vast space of all possible anomaly-free local Lagrangians.)
On the other hand now, within the restricted area of Einstein-Yang-Mills-Dirac type theories, it currently seems that by choosing suitable worldsheet CFTs one can obtain a large portion of the possible flavors of these theories in the low energy effective approximation. Lots of kinds of gauge groups, lots of kinds of particle content, lots of kinds of couplings. There are still constraints as to which such QFTs are effective QFTs of a string perturbation series, but they are not well understood. (Sometimes people forget what it takes to define a full 2d CFT. It's more than just conformal invariance and modular invariance, and even that is often just checked in low order in those "landscape" surveys.) In any case, one can come up with heuristic arguments that exclude some Einstein-Yang-Mills-Dirac theories as possible candidates for low energy effective quantum field theories approximating a string perturbation series. The space of them has been given a name (before really being understood, in good tradition...) and that name is, for better or worse, the "Swampland".
For this text with more cross-links, see here:
http://ncatlab.org/nlab/show/string+theory+FAQ#RelationshipBetweenQuantumFieldTheoryAndStringTheory
Best Answer
Goals one wants to achieve with those two theories are similar.
We know that superstring theory is a potential theory of everything. One may want to ask what is the difference between the string-net-liquid approach and the superstring approach? Our understanding of the superstring theory has been evolving. According to an early understanding of the superstring theory, all the elementary particles correspond to small segments of superstrings. Different vibration modes of a small superstring result in different types of elementary particles. This point of view is very different from that of the string-net liquid. According to the string-net picture, everything comes from simple qubits that form the space. No qubits no space. The "1" qubits form string-nets. The strings can be as long as the size of universe, which fill the whole space. Light (photons) correspond to the collective motion of the large string-nets and an electron corresponds to a single end of string. (See a picture of string-net "vaccum". See also a talk) A modern understanding of the superstring theory is still under development. According to Witten, one of the most important questions in superstring theory is to understand what is superstring. So at this time, it is impossible to compare the modern understanding of the superstring theory with the string-net theory. In particular it not clear if the superstring theory can be viewed as a local bosonic system (ie a qubit system). The string-net theory is fundamentally a local bosonic system (ie a qubit system).
So, if superstring theory is a qubit model (or a quantum spin model in condensed matter physics), then superstring theory and the string-net theory is the same, since the string-net theory is a qubit model (or a quantum spin model in condensed matter physics).