So you are asking what is the difference between going from just talking to someone/going on dates/being single to actually declaring that you are in a relationship with a person?
Firstly, I believe it would be sound to lay the guidelines for the framework of a relationship. I would ask what kind of relationship the other person likes to be a part of. I would say there's a bunch of different relationships out there.Casual, serious, long-term, short-term, monogamous, polygamous, platonic, intimate, blah blah blah blah. Find the words that would most accurately describe your relationship.
For instance, someone seeking a long-term, serious, monogamous relationship may or may not become offended that you are accepting numbers from other guys. It depends on his expectations of you as a partner. Speak about this with him. Some guys wouldn't be offended because they do not feel threatened. Others may perceive that as an act of disrespect. Communication is the lifeblood of any type of relationship you have. We cannot read minds.
I believe it is essential to tell the person that I'm dating what I want out of a relationship so that they may make the necessary preparations (or not) to enter into the relationship that I find appealing. I would ask my potential partner the same thing. Just ask them what they want out of a boyfriend and what they don't want out of a boyfriend.
I personally don't like it when the guy I'm with is getting the phone numbers from guys that obviously are interested in him and try to pursue my partner in my face, and if my partner knows how that makes me feel and does it anyways then I take it as a form of disrespect. Other people may not be that way but you just have to ask them.
Bold text is the shortened version that doesn't repeat itself over and over. lol