I think we use know for either, but use it as a comparison with something more definitive. Examples;
1. I know him (we are a school), but I don't really know him.
1. I recognise him, but I don't really know him.
1. I know him by sight, but I don't really know him.
1. I know of him, but I don't know him. <-- more distant
2. I know him, but I am not very familiar with him.
2. I know of him, but I am not very familiar with him. <-- more distant
2. I know him, but we're not buddies.
2. I know him, but we're not friends.