Interesting - colloquial sloppy use of an originally precise language?
'I am sorry' (from 'sorrow') to me (!) means that I have indeed a feeling of regret for what I am or was doing or of commiseration;
'Excuse me' is asking (in that wording demanding!) for forgiveness - it's mostly presumed to be granted, though that actually should not be self-evident.
(Simply test by answering 'NO' in any circumstance you're addressed with 'excuse me' - it baffles people all the time)
