☆.A.
Too hard to say from the vague info given.
Depends...on a LOT.
There can be MULTIPLE reasons for apologies.
Kind of like Sybil, ya know?
I think in what you've mentioned the "I apologize" was more like "didn't mean to tick anyone off" than "I'm truly sorry for what I said and have given it much thought and have completely changed my opinion on the subject" -- a "smoothing of ruffled feathers.
I don't think there's a greater sincerity by using the words "I'm sorry for x y z" rather than "I apologize" at all. Same thing. Same meaning.
You can't DEMAND apologies--if you do, they're not sincere, most likely.
Apologies are for the giver, not the receiver...Psych 101.
Good rule of thumb:
A lways
S ay
S orry
And mean it! Otherwise, don't bother, right?