Both, but to really understand that you need to think about what “color” really is. Color is not a physical, objective thing. Light has a certain frequency but that isn’t what color is, color is a *sensation*. You can see the same color with a specific frequency of light and with a combination of several different frequencies and intensities (think how a screen produces colors only using red, green, and blue lights). Color is how your brain interprets sensation and this influences what it means to say a creature can see “more colors”. Picking up on the differences between stimulus is one way to actually see more colors.
Humans sense color based on the varying stimulation of three different kinds of light-sensing cells, each most sensitive to a different frequency of light. Mantis shrimp have 12 different kinds of light-sensing cells which means they have the ability to distinguish between many more different colors within the same frequencies of light that humans can see. But their visual range also extends beyond that which humans can see into ultraviolet light, as well as being able to distinguish the polarization of light which humans cannot.
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