What is the difference between "have an affair with somebody" and "cheat on somebody"

Did you have an affair with her?
Did you cheat on her?

Does both have the same nuance?

Solution 1:

Using the "normal" meanings of the terms --

If you "have an affair with Betty" you are regularly seeing her (in a sexual intimacy sense) clandestinely. You may or may not have a "significant other" who is unaware of this relationship.

If you "cheat on Ruth" you are having intimate relations with someone else.

So you can simultaneously have an affair with Betty and cheat on Ruth, but you cannot (without playing some games with words or emotional implications) cheat on Ruth by having an affair with (the same) Ruth.