Difference between Sentinel - 2 data acquired from AWS S2 bucket and GEE

Not sure which of the AWS S2 buckets you are looking at, but the source of the difference is almost certainly related to new baseline, which introduced an offset (description was available here until recently, but is no longer available).

The “main” AWS S2 bucket keeps data as they are produced by ESA

Thank you.
Yes, I was referring to the bucket you linked to in your response.
Could you please elaborate or give different source to the offset you refer to since the link is broken? or did you refer to the difference mentioned here?

Yes, this is the same thing - GEE does “shift range by 1000”, whereas on AWS the data are stored as produced by ESA.

But is the data stored on AWS is the L2A product?

This one indeed is:
arn:aws:s3:::sentinel-s2-l2a