When you look at a spectrum, you're using some kind of optical effect to spread out the different frequencies of light. Most commonly this is done by a triangular prism, where the difference between the speed of light in air and the speed of light in the prism material ('refractive index') causes different frequencies of light to bend by different amounts. Generally, lower-frequency red bends least and higher-frequency violet bends most, with the other colors spreading to varying amounts between the two.

Depending on the refractive index difference, the amount of bending changes. One kind of prism (say, clear plastic) might be rather weak so that the difference in angle between red and blue are very small, producing a very narrow rainbow, while another prism can use a better material and spread red and blue onto very different angles, giving you a wide rainbow. Both of those are real and valid spectra. Neither is more "correct" or "real" than the other; it's just different materials spreading out the light to different amount.

And then of course the actual size of the spectrum produced depends on how far the target wall is from the prism. A prism that produces a very wide spectrum with a wall that's only two inches away will have a narrower resulting image than a less powerful prism projecting on a wall ten feet away.

This question seems bit like looking at an 18" television and a 50" television and asking "But which one is showing the real TV signal?" The question doesn't really make sense.

When you look at a spectrum, you're using some kind of optical effect to spread out the different frequencies of light. Most commonly this is done by a triangular prism, where the difference between the speed of light in air and the speed of light in the prism material ('refractive index') causes different frequencies of light to bend by different amounts. Generally, lower-frequency red bends least and higher-frequency violet bends most, with the other colors spreading to varying amounts between the two.

Depending on the refractive index difference, the amount of bending changes. One kind of prism (say, clear plastic) might be rather weak so that the difference in angle between red and blue are very small, producing a very narrow rainbow, while another prism can use a better material (such as a diamond) and spread red and blue onto very different angles, giving you a wide rainbow. Both of those are real and valid spectra. Neither is more "correct" or "real" than the other; it's just different materials spreading out the light to different amount.

And then of course the actual size of the spectrum produced depends on how far the target wall is from the prism. A prism that produces a very wide spectrum with a wall that's only two inches away will have a narrower resulting image than a less powerful prism projecting on a wall ten feet away.

This question seems bit like looking at an 18" television and a 50" television and asking "But which one is showing the real TV signal?" The question doesn't really make sense.