There is a difference though there may not feel like there is so it would be hard to sort out. I am guessing that what is being considered is for you to think about the intention behind not hugging and saying it would have to be metaphorical. If this is a standard policy or something that in the moment was felt to be the most appropriate response, then it is clearly not intended as rejection. It may feel that way regardless. Therapists tend not to do things that are deliberately rejecting toward their clients. That sorta crosses purposes with what they are supposed to be doing. But therapists do have feelings and reactions and may do things that are not always the best for the client.

Even if that happens, it is still open to repair. Lots can be discussed and worked through, even when there has been a very upsetting interaction. In fact, sometimes that rupture/repair works to strengthen the relationship. Not saying you have to consider it. just saying that it is possible.

Once my therapist actually said to me over the phone, "I don't really like you very much right now." You would think that that would have lead to leaving, especially since I was in crisis and needed support. But though I didn't like it, I understood that he had reached a certain limit, that I had been acting out, and that I wasn't being so easy to get along with. He told the truth. I didn't take it as rejection but as his expression of being worn thin. To qualify that though, we had many years behind us and were going through something unusual so I didn't generalize it to his overall attitude.