general relativity - Are all black holes singularities identical?

There seems to be a problem between a singularity and the event horizons size. My logic is this if u have two collapsing stars with different masses there horizons will be different in diameter yet both singularities are said to be the same infinite density points. This would make them to be identical structures since theres no difference between two infinite dense points. So how does one have a larger horizon. And another problem is that theory says that light coming from the collapsed star inside is curved back in what is converging light rays but if this is the case then why does the horizon become larger the more matter the black hole consumes. Shouldnt the light within curve even more since more mass is introduced and shouldnt the horizon shrink instead of grow?