In this context, it's the same difference as between "they were eating salad" and "they ate salad".
You seem to be confusing the two meanings of "go crazy":
1 : to become mentally unsound
I must be going crazy. I can't find my car keys anywhere.
2 : to act in a way that is out of control : to act wildly
We were just talking when he suddenly went crazy and started screaming.
The crowd went crazy when the team won the championship.
The first definition refers to a gradual change in mental faculties, not to any behaviour. The second refers to wild behaviour, not to mental faculties.
Fans "going crazy" nearly always uses to the second definition. It doesn't mean anything gradual happens to them, but that fans behave in an uncontrolled way, which is typically screaming, waving hands in the air, jumping up and down, etc. This behaviour is typically sudden, not gradual, say when the pop star first appears on stage or when a favourite song starts.
So the only difference between your first and second sentences is the timeline during which the fans scream and such. Did it happen at a moment the past, or did was hit happening over a span of time in the past?
a. I was at a Taylor Swift concert and the fans were going absolutely crazy the whole time!
b. Taylor Swift came on stage and the fans went absolutely crazy!
Sentence (a) focuses on a span of time during which the fans went absolutely crazy. Sentence (b) is part of a narrative of what happened at a finished time in the past, same as the "salad" examples above.