What does it mean if a guy doesn't call you his girlfriend?

I have been seeing this guy for four months. He casually referred to me as his girlfriend once or twice (to me), and when I asked him if I was his girlfriend, he quickly changed the subject. A mutual friend recently overheard him refer to me as a friend (instead of girlfriend).

We had one conversation recently in which I told him that I think we want different things and should stop seeing each other, and he made it very clear that he wanted to do what it takes to make things work between us. So if that’s how he feels, why on earth would he still refer to me as just a friend?

I would feel really silly asking him about this (“X said you called me a ‘friend’ instead of ‘girlfriend’ to Y!”) so I was hoping to get some perspectives, maybe from people who have been in similar situations.