I always thought self promotion was being honest about your achievements, whereas self aggrandizement is more embellishing to differeing degress, the levels of success you have had etc.
Let me give my little life story and see which reads better (and therefore percieved to be more genuine.
I feel fortunate enough to have some gift to develop skills quickly but I wish I was not a jack of all trades type. I have beaten Darren Appleton (World Pool Champion 2012) in a 9-ball match, I played well but was given a 6 start to 12. I have also beaten Andy Jenkins when he was ranked #6 in the world at darts, but he was unprofessional in turning up drunk, and played poor allowing a bus driver to beat him. I have also beaten a FIDE master and an International Master at chess in simultaneous displays, but these were on the internet with no real importance and contained some blunders.
In music I have been invited on stage to play a song with a friends band to only find out that the keyboardist/trumpet player was in The Beautiful South and has played on #1 hits.
OR
I am lucky enough to be gifted to succeed at anything I try my hand at. I have beaten Darren Appleton (World Pool Champion 2012) in a 9-ball match. I beat him 12-4 and didn't miss a ball match which angered the hell out of him. I have also beaten Andy Jenkins when he was ranked #6 in the world at darts, I won 5-4 but was 4-2 down and showed a lot of heart to battle back and win. I had only been playing 8 months, that is how quick I developed my skills! I have also beat a FIDE master and a Womans Grandmaster (note: this is only International Master strength) in simultaneous displays, playing lines which I was more prepared in than they were and subsequently won me the game.
In music I have played with some quality musicians including the trumpet/keyboardist from The Beautiful South which demonstrates that I am good enough to hold my own with any musician.
Which one sounds better and more genuine to you? Maybe my first one is more self-deprecation than promotion, but it's certainly more honest and truthful!