My jumps on ice are definitely higher than my off-ice jumps (especially my flip, which is huge on the ice and practically impossible off ice). The reason is that building up some speed and then either picking and vaulting (for flip, lutz or toeloop) or rocking up to the toepick (for waltz, salchow, loop or axel) converts that speed into jump height.
With my axel, I don't really use speed on the ice to give me more height; I simply need to jump higher because I'm wearing those big, heavy skates and I don't cross my shins in the air like I do on the floor in sneakers. That means I rotate slower in the air on my ice axel and can't complete rotation unless I give myself more air time.