Heck, when I was in college, my part-time Starbucks job gave me good health coverage and a bunch of other perks that my first few post-college tech jobs didn't. (This was mid-90's). FWIW.
Seems like it is common enough to have a name.
I might misunderstand you, but progressive tax brackets mean you pay extra money only on money earned after the limit. So if that line is $1000, under which the tax rate is 10%, you pay $100. Then if the tax rate above that is 20%, I pay that much only on the amount above $100. So if I make $1020, I pay 10% * $1000 + 20% * $20 = $102. (Not 20%*1020 = $204)
In other words, you can’t take home less money overall just because you crossed the line into a higher tax bracket. I felt it was worth mentioning because it’s an easy misconception to have.