What determines if a photon is displayed as light or not? A photon is the particle of light. But a photon is also a force carrier and plays a role in many other situations. What I don’t understand is what determines if it shows up as light or not? Is it just a high concentration or pattern? Why don’t photons show up in all situations?
 A: Photons are present in all electromagnetic interactions. Sometimes they are virtual (e.g., in the case of electrostatic interactions), and sometimes real (e.g., in the case of electromagnetic radiation). For a photon to be perceived as light, it must a) be real; b) have the right range of wavelength (or frequency, or energy); and c) must be detected by your eye (or another light detector). 
A: The other answer is correct. Let me add a few things.
Photons are the quanta of light, and the quanta of energy, that is, the smallest amount of involved in an interaction.

In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization".[1] This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.
  For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation).

https://en.wikipedia.org/wiki/Quantum
Light is a type of EM waves ( we use light for visible and invisible), but EM waves include all other wavelength, including for example radiosignals.

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy.[1]

https://en.wikipedia.org/wiki/Electromagnetic_radiation
That is I assume you are asking about visible light, and in that case it does not matter what the number of photons actually is reaching our eyes (or a detector), since the human eye can detect single photons (though to actually perceive it you need more).

The human eye is very sensitive but can we see a single photon?  The answer is that the sensors in the retina can respond to a single photon.  But neural filters only allow a signal to pass to the brain to trigger a conscious response when at least about five to nine arrive within less than 100 ms.  If we could consciously see single photons we would experience too much visual "noise" in very low light, so this filter is a necessary adaptation, not a weakness.

http://math.ucr.edu/home/baez/physics/Quantum/see_a_photon.html
You are asking what determines whether photons are called light or not.
So photons make up all (are the quanta of) EM waves, certain wavelengths are called light (in your case visible), and in the case of visible wavelength our eyes (or a detector) can detect even single photons.
A: At our present understanding of physics, photons are elementary particles, in the axiomatic table of the standard model of particle physics. This model is mathematically based on quantum field theories.
The understanding is that the underlying layer of nature is quantum mechanical, and all classical theories are limits, emerge from this underlying level. A bit how thermodynamics can be shown to emerge from statistical mechanics.
It can be shown that the classical electromagnetic wave,light, emerges from a quantum mechanical superposition of zillions of photons. And not only the frequencies of visible light, but all electromagnetic waves are a superposition of photons that have energy$=h*ν$, where $h$ is thePlanck constant and  $ν$ the frequency of the emergent classical wave.

What I don’t understand is what determines if it shows up as light or not?

As discussed above, a photon is a building component of electromagnetic waves, of which visible light is a small part of frequencies. It is never by itself "light". Light needs the superposition of very many photons in order to emerge as a perception.

Is it just a high concentration or pattern?

It is high concentration and the mathematics of wavefunction superposition that make what is called "light"

Why don’t photons show up in all situations?

They do, but they are so dense that special experiments are needed to display their existence.
This single photon double slit experimentt may help in understanding how single photons add up to a phenomenon that becomes a light pattern.
