Also The T-1000 murders people prior to the reveal, while Arnold doesn't.
Anyway for the T2 twist, I always just assumed that when T1 was shot, Arnie was kinda unknown, but by T2 he was a pretty big Hollywood action star and couldn't be the bad guy anymore. So they had to wrangle him being the good guy into a sequel if they wanted him back.
Such a good scene, and captures a window into the terror and deadly force we add to our own society, just a corner gunshop visit away.
Kinda reminds me of my top-3 favorite TV shows ever, Person of Interest. The protagonist there had a habit of knee-capping the criminals instead of shooting to kill, which seems like the more humane alternative, but the more I think about it, the less I'm sure.