Another thoughtful question.
To me there is intimacy in both, but with friendship it just may be a bit more personal. My friends are the few people I confide in. They are the ones who get to hear the nitty gritty of life and all it's challenges. They are the ones I process things with in a more personal way. They're also the ones I go to when there is something to celebrate. It's a mutual relationship of trust and love.
Fellowship is wonderful also... It's the ladies I do bible study with and people I see in church, perhaps people I even just meet throughout my day. We can encourage each other and lean on each other for many things, but not really personal.
These differences for me exist because the friendship relationships are closer.. They've developed over many years and hardships, and a level of trust has been built. The fellowship relationships exist for different reasons and both are beneficial. It's healthy to have a close network of people to trust and confide in, but not everyone deserves that honor.
Fellowship relationships can and do grow into friendships... but I think it takes time.
I just reread your question, and I realize I didn't really answer it.. :-)
Yes, it's ok to reject a friendship of a church member. Yes, I believe you can still fellowship. There is still something to always learn... and to teach. I don't see a reason why this mutual give and take relationship couldn't exist unless it is toxic.
What a beautiful response HandMaiden. I look forward to hearing from you more on here.