I'm 22 he's 32. I said I'd never date a man with such age difference but now I understand why some ppl say....?

age doesn't matter. I am really into him. He does not want to use the terms girlfriend and boyfriend nor dating. But he's with me everyday and most of my weekends for the past month or so. I have had commitment issues in the past so I kinda like the idea but.... and you knew there was a but right.... He uses the word friend. (like nothing special nuh) but of course he calls me babe and boo. I am just a little concerned that ppl with not respect our relationship since we have not said that we are dating or anything. He also had expressed the desire to keep it exclusive. Oh and of course there is PDA which is weird for me cause i'm not really into that since my first BF. and he said he isn't normally into it. But we do it anyway and he isn't afraid to be with me infront of ppl. Everyone that sees us gets the understanding that we are together. I am just wondering if maybe not using terms to describe our relationsip will be come a problem for us both. What's your opinion.