As the Wikipedia article you linked to says,
Terahertz radiation refers to electromagnetic waves propagating at frequencies in the terahertz range. [...] The term typically applies to electromagnetic radiation with frequencies between high-frequency edge of the microwave band, 300 gigahertz (3×1011 Hz), and the long-wavelength edge of far-infrared light, 3000 GHz (3×1012 Hz or 3 THz).
So this radiation is simply a particular type of electromagnetic radiation, identified by the fact that it has a frequency within a particular range. Other than the frequency (and consequently the wavelength and photon energy), it's no different from any other electromagnetic radiation.
The EM radiation that makes up visible light has frequencies about a thousand times higher than this range. That's why visible light is not called terahertz radiation. And (most of) the infrared radiation emitted by objects at the temperatures typical on Earth has a frequency around 10 times higher than the terahertz range.
If some device that emits terahertz radiation could have the frequency of that radiation adjusted upward by a factor of a thousand or so, it would be emitting visible light. The spectrum (and color) of the light emitted would depend on the device.
Short answer:
- Proteins or photopigments involved in vision have different sensitivity to light
- The transduction paths are different or the paths to produce/mantain the proteins/photopigments.
Generic answer:
The proteins or photo pigments responsible for sensing light usually undergo a conformation change/chemical change induced by light, but this change depends on the wavelength of the incident light. There are many different proteins that are light sensitive and the reasons why this reaction happens on a specific wavelength interval and what kind of reaction happens depends on the protein.
However, not only different proteins react differently to light, but also what happens next may be different. After the protein suffers a change because of light (whatever that is) a long chain of chemical reaction begins which will end up as an electrical signal. Also, usually proteins or photopigments have to be recycled after being activated/bleached, which is done by parallel biochemical pathways. Mistakes on these paths will also after the ability of seeing a specific colour.
Example:
There are many kinds of vision mechanisms in the animal kingdom. The colours (sets of wavelength intervals) that each animal sees highly depends on the set of proteins that these animals have and the transduction path after the proteins are activated. We humans, for example, are good at seeing green and other colours that help us to identify food that we usually eat [1]. Interestingly, even small changes on the aminoacid sequence of the proteins change its sensitivity for light. For example, some people have cones (some of the cells responsible for vision in humans) with photo pigments that are sensitive at 530 nm and some people are sensitive at 562 nm. This difference is caused by only 3 aminoacids substitutions in a protein [2]. Another example involving the recycling pathway of a photopigment can be found at [3]. It was observed that some mutant Drosophila flies had their vision impaired because they could not keep the concentrations of the visual pigment Rhodopsin.
[1] Surridge, Alison K., Daniel Osorio, and Nicholas I. Mundy. "Evolution and selection of trichromatic vision in primates." Trends in Ecology & Evolution 18.4 (2003): 198-205.
[2] Neitz, Maureen, Jay Neitz, and Gerald H. Jacobs. "Spectral tuning of pigments underlying red-green color vision." Science 252.5008 (1991): 971-974.
[3] Ostroy, SANFORD E. "Characteristics of Drosophila rhodopsin in wild-type and norpA vision transduction mutants." The Journal of general physiology 72.5 (1978): 717-732.
Best Answer
One can give a highly qualified, but definite "yes" in answer to your question.
Contrary to popular belief, if it weren't for the UV, then staring at the Sun would not be a particularly hazardous thing to do for the majority of people. This is why I said "highly qualified" - for people with certain conditions, simple staring at the Sun may be hazardous, even aside from the UV (more below).
There are two ways that light will damage your eye:
Fairly obviously from the nomenclature, the first kind (1) of damage is where so much energy is concentrated on the retina, its temperature is raised and the tissue is damaged or destroyed. The second kind (2) is where the light's photons are energetic enough to beget chemical changes by breaking bonds in organic molecules. This can lead both to acute poisioning of and damage / destruction to the tissue by the weird molecules / free radicals that come out of such light-matter interactions and also long term damage, even nuclear (in the sense of cell nucleus) changes, dysplasia (e.g. cataracts) and ultimately neoplasia (cancer).
The retina in the mammalian eye is superbly, densely envasculated. You won't find a better liquid cooling system in our contemporary human primitive technology. This situation has arisen from two evolutionary drivers: (1) the retina is simply adapted brain tissue, and the brain itself needs sophisticated liquid cooling: of all the organs it is the most sensitive to deviations from the warm blooded homeostatic temperature ($37{\rm ^oC}$) and (2) since we are creatures of the Neogene Eastern Africa, accidental looking at the Sun was everyday and commonplace to us.
Therefore, if you stare straight at the Sun at high noon, your pupils will have shrunken to about $1{\rm mm}$ diameter, thus the power incident on the retina is of the order of $\frac{\pi}{4}\times 10^{-3}{\rm m^2} \times 1000{\rm W} \approx 1{\rm mW}$. This is WAY less than the normal, healthy retina's capacity to dump heat, even if concetrated into a diffraction limited spot. The uncomfortable feeling you get from looking at the Sun is mostly a psychological one: if you did it for thirty seconds, your retinal cone and rod cells would be so drained of ATP (energy stores) that you would be totally (albeit altogether temporarily) blind for many, many minutes. For either a predator or prey creature (we are both), this is not good. But the intensity alone, although it causes severe, but temporary blindness, is not a hazard (as long as you don't get eaten by a Neogene lion wearing sunglasses, or fall over a cliff texting on your phone whilst your sight recovers when the receptors finally get their ATP levels topped up). As you rightly point out the danger from the Sun is UV: it is not the intensity with the uncomfortable, squinty-eye feeling that arises from it that is the danger for someone with a healthy retina. It is the low level but constant UV dose one gets mostly from scattered light that is the problem. This is why sunglasses in many countries must by law fulfil stringent UV attenuation performance standards: sunglasses stop the "glare" but this is not the danger; indeed the "comfort" afforded by non-UV attenuating lenses is a very false sense of security.
Three other points about the Sun's power delivered to someone who stares at it.
Some eye conditions mean that even the thermal loading on the eye from the Sun can be dangerous. Macular degeneration is a major one, as is albinism or even an extremely white complexion. Heart and circulatory diseases are others. Other diseases and defects mean that the pupil cannot respond to high light levels. Many recreational drugs can dilate the pupils severely, particularly hallucinogens like LSD, psylosin or mescaline can lead to eye damage in this way.
Interestingly, if you begin with the assumption that the Sun's intensity into a fully shrunken pupil of someone staring straight at the Sun represents a safe upper limit to power dose (in the absence of UV), then you come up with dose limits that pretty closely match the ISO60825 laser safety standards for visible light.
The last comment is particularly relevant to you. ISO60825 does NOT tell the difference between coherent and incoherent light. You tread an LED exactly as you would a laser: if you apply ISO60825 and determine that the light dose from your LED is intrinsically safe (i.e. class 1), then this is a sound indication, aside from in severe cases of the diseases I mention above. The other factor I haven't mentioned is the blink response, which is also accounted for by ISO80625, but this sets levels for class 2 and class 3A, which are not intrinsically safe, but which are deemed to be low enough that an accidental looking into the beam will not be harmful owing to the shielding afforded by a healthy blink response (assumed to limit the light dose to 0.25 seconds). Again, drugs severely interfere with this reflex.