Personally I can jump anything on any type of horse, even if I’ve never jumped that high, because I have no fear and kind of get a thrill from it, I love an adventure when it comes to horses (traumatised if heights and spider though)
With my own pony, I need to build trust with her and bond with her before I get enough confidence to jump her because she is a little hot and I am a slightly nervous jumper anyways. If I was riding someone else pony and they told me what their horse was like I could nearly jump then no problem, with enough encouragement from the owner haha
I at least like to know the horse relatively well before I do anything too dangerous, but once I have flatted and jumped them a bit, I can do most things as long as it is a horse I am comfortable with.
Both types are totally fine, nothing wrong with needing to trust and bond with your horse first before doing different things. And being courageous and doing new things on a new horse or a horse that you don't completely new is also amazing! I'm personally the "can jump and do anything on any type of horse" rider but thats just me!