Knievel has it. I add only a few examples.
Also, As he said, Jiwon has something confused about "require" DOES NOT EQUAL "given".
Guests are required to wear a tie. = you will not get in without a tie.
Guests are requested not to feed the birds. = please don't do this.
So, as above
Request is similar to ask, some idea that you do not have to.
Require is similar to MUST, or need, you MUST do this.
Obviously, many signs with these words do not mean this at all. Many times, a sign will say "patrons are requested to ..." & likely they actually want you to do it. Similarly, "requirements" are often ignored.
The difference on a sign is how forceful, they want the sign to appear.
As, I said, Knievel, basically explained it.