“My friend” is like a pronoun, “I told my friend about my plans”, in that sentence you could use any other pronoun like “I told her about my plans”. “Friend of mine” is like a direct object, “She is a friend of mine”, here “she” is the subject of the sentence, “of mine” is a prepositional phrase that specifies whose friend she is. I hope it helps, :)

This topic comes up periodically. Here is an excellent explanation by Su.Ki. from https://www.italki.com/question/477939. [text] 'My friend' is specific. 'A friend [of mine]' is non-specific. If you say 'my friend', it implies that the listener or reader already knows who this friend is - maybe the speaker only has one friend, or they have only one friend in a given context or they've already said who this friend is. (The same as if you said 'My dad' or 'my boss' or 'my boyfriend/girlfriend' - we'd know who this person was). When we say 'a friend of mine', it means 'one of my friends' i.e. just one of several. It's normal to use the phrase 'a friend of mine' the first time the person is mentioned, and thereafter just 'my friend'. For example: 'I went shopping with a friend of mine last week. We were just getting off the bus, when my friend suddenly said...' If you began the story by saying 'I went shopping with my friend ..', it wouldn't be wrong, but it would be a little odd.

"My friend" sounds a bit more personal, but they're interchangeable in most cases. Examples: My friend and I are going shopping. A friend of mine and I are going shopping. My friend is coming over tonight. A friend of mine is coming over tonight. John is my friend. John is a friend of mine. She has been my friend for years. She has been a friend of mine for years. These are all correct and things I would say as a native speaker. I hope this helps!

'My friend' is more informal and can also imply that the speaker has spoken about this person before. For example, my friend Jane.... etc 'A friend of mine' is far more formal and is completely disconnected to the person to whom you are speaking - they have never heard of them being mentioned before. Siobhan :)