"Later" just means "Wait until I tell you to do it."
As of 10.5, however, anything that requires a restart will not actually install until all users have been logged out in preparation for a restart, so it's essentially the same thing as "on next restart." (This doesn't apply to updates you download manually, only Software Update.) I assume Apple did this to prevent problems from updating the system while the files are being accessed. I can't actually remember, but I think if there are updates downloaded and ready and you shut down or restart, the system will prompt you to install updates while you're at it.
Either way, I can't think of anything short of a hardware issue that would cause slowdowns after a restart vs. a full power down. Do you have any external devices past a keyboard and a mouse? Maybe one of them is glitching out and causing slowdowns until power is killed to it completely so it can re-initialize (which is the only difference between shutdown and reboot, so far as I can think of).