It doesn’t necessarily have to be either one of those scenarios. The best place to begin is by sharing your concerns with your therapist. Talk to him about how you love him but have not yet fully internalized your relationship with him.
The two of you explore this and work through it. It may be that it’s just fine the way it is and you’ll keep getting good work done. It might also be that part of the problem is that the two of you aren’t a good fit. Either way, your therapist should be able to help you sort that out and then take action based on what’s best for you.
You shouldn’t need to be in therapy indefinitely unless that is something you want to do.