Well if you want a quick and dirty explanation of the difference here you go.
A drill just spins the bit and can go anywhere from really slow to really fast.
A hammer drill spins the bit just like a drill, but now imagine using a hammer and a chisel on a concrete wall. You hit the head of the chisel with the hammer and break off a small chunk of the wall, then you turn the chisel a few degrees and hit the head again. Now imagine doing this thousands of times a minute.
A rotary hammer is like the bigger cousin of the hammer drill. It can hammer more powerfully.
For an impact driver, imagine using a wrench on a nut, then take a hammer and hit the wrench to turn the nut a few degrees. Repeat over and over. This is basically what an impact driver does.
There are trade offs between an impact driver and a drill. An impact driver usually turns slower, especially under load, but you can get enormous torque. Generally you need to use special unhardened bits/sockets with an impact driver, if you use hardened bits they can shatter.
Also with any hammering or impacting device you want to use hearing protection.