Which word should I use talking about people wanting to show affection for each other like a couple?Cuddle and snuggle imply closer bodily contact of longer duration. They would happen between people who are very intimate. A hug is an embrace -- arms around each other -- and doesn't carry the idea of protracted contact that snuggling and cuddling do.
Off the top of my head.
A cuddle is a prolonged, more active hug. You cuddle children, lovers etc. A hug isn't as commited or intense, it's just friendly.
You usually 'snuggle up' in bed or 'snuggle up together' when you're cold.