A little bit of both honestly. When you fall off you immediately know if you really hurt yourself, you either are fine (a little sore of course, but okay otherwise) or you are in pain and you know something happened. If I’m fine (which is 99.9% of the time) then I’ll stand up and get check my horse. If you actually injured yourself you’ll know right away. In that case I would stay where I was because I wouldn’t want to aggravate the injury, but I would watch my horse to make sure they’re okay as well.
Hope this answers your question!
The horse. I always check to see what damage has happened to the horse because then you will be more assured.