If you request something, you ask for it politely or formally.

If you request someone to do something, you politely or formally ask them to do it.

If you make a request, you politely or formally ask someone to do something.

A request is a song or piece of music which someone has asked a performer or disc jockey to play.

If you do something at someone's request, you do it because they have asked you to.

If something is given or done on request, it is given or done whenever you ask for it.