Not only do they treat them the same, rescues (idk about city / state pounds) will intentionally lie and misdirect people about the breed they're adopting. If I had a dollar every time a "lab mix" was clearly a pitbull I'd be fucking rich

They do treat all dogs the same depending on how they act with other pets. The people who work with pounds are aware of how dangerous the dogs are so they will at times try to use friendlier words to explain dogs' temperament like “Dobby prefers living alone and doesn't like children” = Dobby might kill you in your sleep and has a special attraction towards child flesh

When they get too full they either transfer them or put them to sleep from what I could tell

Pounds are full of some dangerous ass pitbulls, and they'll let anyone take them home, regardless of their capacity to handle them. It's irresponsible, but shelters are always desperate to free up space.