As mentioned, the jump gets higher, it also gets wider, the stride gets longer. That changes your perception of where you need to be for take off and maintaining your pace off the corner to a fence. It really is about managing that canter. Lower fences let you get there too long or too deep, mess with them the last couple of strides, speed up, slow down and have the horse still get over the jump. 3’ off a 12’ stride is about where it gets harder for the horse to jump despite you and maybe just say no via stopping or a buck on landing.
Also, at shows, once you get to 3’, you start seeing combinations and in and outs on the Hunter courses normally not used below 3’. Thats the first height you get exposed to USEF rated course design questions, even most locals use these guidelines for Hunter course construction.
So, you are going a little faster, the fences are a little bigger, little wider and the courses a little more challenging. But you don’t really do anything different, it is very much in your head. But everybody goes through a period of adjustment every time they move up. You need to expect it and work through it.
Need to point out at that another thing that can happen when you move up is you find out you cannot simply work through it because the horse can’t do it and/or your trainer has reached the limit of their ability to help you. In other words, you riding ability has outgrown the horse, trainer or both. People forget this or go into denial but it’s a big reason simply moving up a level can be such a struggle. Wanting to move up can lead to other, more difficult decisions.