Do restaurants use bags of shredded carrots for carrot salad or do they shred their own?

It depends on the chef. Restaurant chains most likely buy their veggies pre-cut.

I’ve seen workers in restaurants just cut open bags of shredded carrots and salad greens right on the chopping boards with their knives and use those. These looked like the same kinds of baggeed veggies that you or I could buy at the supermarket.

I totally depends on the restaurant. Some brag that their veges are prepared fresh, on the spot. Without such a claim, I would suspect they buy them in bags from restaurant supply stores.