No, They both mean little or no chance of success. Fat chance is the ironic form and slim chance is the direct form. Irony means you say something but mean the opposite.Another idiomatic way of saying this is "no way" John

'Fat chance' is the sarcastic form of 'slim slim' chance. If I said 'fat chance of that happening" I would mean that it doesn't have very much chance at all. 'Fat chance' is potentially offensive if a person is asking you about their own chances of success. It is less offensive when talking about a another person or group. "Tom said he'd pay for everybody's drinks. Fat chance of that happening! We all know how he holds on to money." "Maybe your dad will let you go with us on the camping trip." "Oh, fat chance! There's no other adults on the trip." If you wanted to say the opposite of 'slim chance' you would say 'it has a pretty good chance' or 'it's very probable.'