People do remember things differently - some details will have more importance for them, or impact on them.
However, if this is happening all the time, and the other person is behaving or saying things that deny your perspective or your right to have and express your own opinions and thoughts, then that's a major problem.
For a long time with my ex I felt I was going crazy because he remembered things so differently from me. My memory isn't great and I don't always remember the details, and in fact, contrary to what someone said up thread, I would forget entire incidents - possibly because they were so upsetting and traumatic, I don't know. I was friendly with a neighbour and would confide in her, and sometimes she would remind me of things that I'd forgotten all about.
Anyway, for me the ultimate in gas-lighting was when my son was about 6 years old, and was about 6 months after he'd broken his arm. It was a complicated fracture and there were many hospital appointments. Ex took him to one appointment. I did all the rest.
So, we're sitting at the table having our tea, and ex h starts talking to DS about did he remember when they went to get his stookie (plaster cast) off his arm? Ex went into great detail about it - the book they read together in the waiting room, what the nurse said to my son, how brave he was, and so on. DS just looked over at me.
Ex turned to me, and said, "What's up with your face?"
And I said, "But you weren't there when he had his stookie off. I took him."
He denied that, said he'd taken him that time, but that the nurse could only take half the stookie off that day, and I must have got confused and been thinking about when I took him to get the other half removed.
And at that, I had him.
I said, "No, the stookie came off in one go. I was there, I kept the stookie and I know where it is now."
Not anther word from him. He got up from the table, and went out for the evening. This was never mentioned again, but it was as creepy as fuck.
That was actually when I realised that I should be frightened of him. I left soon after.