For me a connection is a good rapport. I feel comfortable talking with/ confiding in them and I feel like they understand me to some extent. The conversation flows and is as a rule is not awkward. Basically, I like and respect them and they feel the same about me. Whether they actually like me or not I wouldn't know, but since I'm hyper aware of people's to me body language and tone, I think I'm a decent judge of that. I don't take it beyond the professional, however. My connection may cause me to care about them beyond the therapy room and I would hope for their wellbeing and feel bad if something bad happens to them. That said, I've never had an urge to give one a holiday gift or card and would never think of getting one from them. So while there is a sincere feeling of fondness, it is still very limited. This has not happened with every therapist I've seen, even if I liked them enough as a T, so it's unique to the person.