How do different colours look in Infrared Light?

They don't look like anything in infrared light. A "true color" infrared image would appear totally black to human eyes.

What we define as "color" is the way our eye/brain system perceives certain wavelengths or combinations of wavelengths from the much broader electromagnetic spectrum. The portion of the electromagnetic spectrum that we perceive with our eyes is called "visible light" or the "visible spectrum."

Infrared light is not visible to the human eye/brain system, therefore no infrared light is perceivable as "color", or even "monochrome" to the human eye. Infrared light is a range of wavelengths of the electromagnetic spectrum that are outside the range of wavelengths that produce a chemical response from the cones in our retinas.

What we see on a screen being fed from an infrared camera is a signal that has been converted to represent various brightnesses of electromagnetic radiation from within the infrared spectrum as various brightnesses of visible light. In the case of false color infrared images, certain wavelengths of the infrared spectrum are reassigned to be displayed as certain colors within the visible spectrum.

The image we can see from an infrared camera is what is known as a false color image. What this means is that a range of wavelengths in the infrared spectrum are rendered with a corresponding wavelength of visible light. Just as with visible light, a particular wavelength of infrared light can vary in intensity from just above black (shadows) to near saturation (highlights).

How each wavelength and intensity of the infrared light is translated into the visible light we can see depends a lot on the purpose and intended usage of the infrared image. It also depends on whether the image was captured with a camera designed from the ground up to record light in the infrared spectrum or with a camera designed to capture visible light that has been converted to capture infrared light by removing the infrared filter found on most cameras and adding a filter to remove visible light.

Images from astronomical instruments that photograph the night sky in infrared tend to be processed so that they look like the visible night sky even though what is visible in the heavens and what is not will be different in an infrared image than what is visible in a visible light image. Typically, shorter wavelengths of infrared light will be rendered as shorter wavelengths of visible light (blue), medium wavelengths of infrared light will be rendered as medium wavelengths of visible light (green), and longer wavelengths in the infrared spectrum will be rendered as longer wavelengths in the visible light spectrum (red).

On the other hand, images used to see humans in the dark ("night vision" images) will often display different intensities of the same wavelength (10µm - the wavelength at which humans radiate the most heat) using different colors. In that case white might denote the highest intensity at 10µm, red might denote a slightly lower intensity at 10µm, green an even lower intensity, and so on. The other wavelengths of infrared light might not be rendered at all.

Examples of each of the above scenarios are visible near the top of the Wikipedia article on Infrared.

Can we differentiate between skin colors in an ir image like we can do in black and white images?

We can't see infrared frequencies. At. All. What you are calling an infrared image is not being displayed using IR wavelengths. It is the result of

• a camera that has collected data about the intensity of one or more wavelengths of IR radiation
• a system that has processed that information and converted it to be displayed using visible wavelengths

How the system has been set up to measure IR and how it has been programmed to shift the values of the information it has recorded will determine the answer to your question.

It is possible for an IR camera and system to differentiate between the IR light reflected by different skin tones. It is also possible for an IR camera and system to not differentiate between the way IR light is reflected by different skin tones. It all depends on what portion(s) of the IR spectrum you are imaging and how you have decided to translate that information to visible light.