Consider the two responses to the question, "Who is he?" in normal conversation.
a. "He is my friend."
b. "He is a friend of mine."
Response a. is defining. It is definite. It implies that you really know the person and value them. It has a stronger feeling of holding the relationship in high esteem because it is using the possessive form. "My friend" identifies the person as a true friend.
Response b. is more vague. It puts the person we are speaking about into a group of people with whom we interact in a friendly manner, but we are either unsure of the value of the friendship (does he still think of me as a friend?) or do not feel strongly about the person. There are different degrees of friendship or different types of friends (work friends, activity friends, study buddies, and friends (I would call them true friends or real friends).
Whether we respond with "He is my friend" or with "He is a friend of mine" can change over time, as the friendship deteriorates or progresses and develops over time. People say friendship is forever, but its expression and even its form adapts to the current circumstances.
Remember the lyrics to the song , Reach Out Of The Darkness by Friend & Lover : “we sat and talked about things on our minds....and now that man ...he is a friend of mine.” It shows the more casual degree of friendship: after one phone call. Who knows, maybe after several years, the singer will be able to say, "He is my friend."