Confused about what lens can fit on camera bodies?

I know that Canon lenses fit on Canon, and Nikon on Nikon, but I'm not exactly sure what mounts are and the EF-S etc. I have a T3i Rebel and I've had my 18-55 f/3.5-5.6 for about two years and recently switched the new 50mm 1.8 STM, and I love the switch. I'm considering about purchasing Canon's pancake EF-S 24mm f/2.8 STM to kind of get a wider angle, as well as using my 50mm f/1.8 for it's focal length. By the way, will that specific pancake lens work on my Canon T3i? Thank you so much to the answer who thoroughly explains mounts, EF-S, what lenses fit on which bodies!

You can put EF lens on EF-S body with no problem. But the reverse is very dangerous.

The distant between the sensor to camera mount is called "Flange Focal Distant (FFD)" or "Back Register". This distant should be equal for both lens and body.

In EF system, the distant is 44 millimetre. But the EF-S *should be* around 30mm. However, Canon decided to keep FFD of the EF-S lens at 44mm and extended the rear part of glass system into the body.

This space is not nothing. It is home of the reflex mirror that bounces the light from lens to the viewfinder so you can see what you want to shoot.

The mirror has to go out of the light path in the instant of picture taking. But if you use EF-S lens on EF body, the protuded part of the rear end will jam this flip-out, destroying the mirror.

The T3i has a Canon EF-S mount so it can use EF mount and EF-S mount lenses. The S in EF-S is for short back focus which is designed for APS-C or crop sensor dSLRs. Here's how the Canon mount system works.

Canon EF-S mount (APS-C) bodies can use either Canon EF-S or Canon EF mount lenses.
Canon EF-mount (full-frame and 35mm film) bodies use Canon EF-mount lenses only.
Canon EF-M mount (mirrorless) bodies can only use Canon EF-M bodies.
Older Canon FD-mount lenses will not mount on any Canon EF variant body without an adapter. FD mount lenses mount on Canon FD (35mm film) bodies. All older (than FD) Canon mounts that behave this way.

Major camera brands like Nikon, Pentax and Sony do not make Canon EF or EF-S mount lenses but third-party lens makers like Tokina, Sigma and Tamron do.

Yes, the 24mm EF-S pancake lens was made specifically for cameras like yours.