If you refuse to do something, you deliberately do not do it, or you say firmly that you will not do it.

If someone refuses you something, they do not give it to you or do not allow you to have it.

If you refuse something that is offered to you, you do not accept it.

Refuse consists of the rubbish and all the things that are not wanted in a house, shop, or factory, and that are regularly thrown away; used mainly in official language.