Here are some examples: I refuse to go with you! My son refuses to eat his vegetables. Politicians refuse to address the real problems of the country. I deny the strength of your argument. Some politicians deny that climate change is real. = They refuse to admit that climate change is real. Notice that the grammar is different. "Refuse" is followed by an infinitive--you refuse to do something. "Deny" is followed by a noun or noun clause (the strength of your argument) or a clause introduced by that (that climate change is real.)

To refuse is to say no to something. To deny is to not admit something, or to not allow something to happen, depending on the context. E.G. Denying entry means to not let someone enter, and to deny that you are tall means that you are saying you are not tall.