A hairstyle is the way you get your hair cut or how you arrange it. If you like to shave the sides of your head and gel up the rest of your hair in a spiky mohawk, that's your hairstyle.
If your hair stylist or barber says, "Do you want your usual hairstyle?" it means they wonder if you'd like the same crew cut or bob you got last time. A fancy hairstyle, which you can also call a hairdo, might just be for a special occasion: "I'll have a curly hairstyle for the prom, how about you?"