I wonder if we just call the "deer fly" a "horsefly" here. We (Missouri, USA) have the little horseflies (maybe a 1/2") and then the giant horseflies (biggest I've caught was 3").
We do have different breeds of them too. Early in summer, the head biting one.
Later, near August, there is one with a yellow back, and it goes for ankles!
That's pants in sock season time.
There are loads of bot flies too. They supposedly go for cattle, but I've caught mice with their larvae, so I worry about napping outside, during their season.
From upstream: Horseflies will happily bite humans, though they are pretty well guaranteed to die in the process.
Not sure this is a deer fly. The ones I hit, often just fall off, then fly away. You usually have to crush them with your foot to kill them. They are tough.
Both have a very irritating bite, but the deer fly is a small sting of pain that goes away quickly while the horsefly tends to leave a large welt that sticks around for at least a day or two.