Qual è la differenza tra Mi paghi un caffè? e Mi offri un caffè? ?Sentiti libero di rispondere con un esempio.

They have the same meaning but they have different weight.

The verb "offrire" which is put in "Mi offri un caffè?" is used to ask politely for the other person to give you something, or in this case to buy you a coffee, but it emphasizes the act of requesting.

On the other hand "mi paghi un caffè?" will only mean "will you buy me a coffee? ", and its meaning it's closer to "will you pay for my coffee? " which is not wrong but a less elegant way of asking for things to other people.

That's why it's better to say "mi offri un caffè?" because you don't put a stress on the fact that your interlocutor is paying.