Neediness and clinginess are synonymous in my opinion. I find someone to be clingy when they literately cling to another like a child who is lost without constant affection and attention. Neediness to me is when someone is very needy when it comes to another person's time, space, warmth, care, and overall presence. This usually happens when you are the highlight of someone's day all day every day. So God forbid something comes up and you can't call or text them back within a certain amount of time, they have a mental breakdown and feel rejected.
I feel like needy is more of like you can't live with out someone like he has to be texting you every minute kind of thing, like you need your own independence clingy is pretty similar, not sure how to explain my views on that like not letting him have time for himself, not letting him have time for his friends, being all over him in public when he doesn't like it, something like that