Pilot reported mistakenly joined up with the wrong aircraft for a formation flight resulting in an NMAC.

Narrative

I departed ZZZ on a pleasure flight with a friend; which was a continuation of several friends flying rides that had been happening all day. I saw what I thought to be one of my friends who was also flying rides; heading towards the airport. I attempted to contact him on the radio; but got no response. This was not uncommon because he used a handheld and often had it turned off when not in the traffic pattern at the airport. We have previously flown in formation and I elected to go try to get his attention and do so again. I flew a wide circle around him and rejoined on his right side and maintained about a 500 ft. distance. We have prearranged signals for doing such things and with the lack of that response and no contact on the radio; I broke off and continued on to a landing at another airport. When I landed I saw him enter the pattern and land also. When he taxied up; I noticed that it was in fact NOT my friends aircraft; but was a very similar paint color and scheme (not the default [aircraft type] colors). I explained the situation and apologized for the confusion repeatedly.