The meanings are not simply semantically different, they are different words representing different concepts.
The register for an event implies the event is recording a list of people who have "registered", and who would be on a "register" of some kind. The register would be checked at some later stage to ensure that only those registered can proceed to the next stage. Register has a very specific meaning and not all events would offer "registration" as an option. If there is no "register" (as in a list), there can be no act of registration. I also disagree with some comments that registration necessarily comes after apply - you may register your interest in some future program, and apply for it when it becomes available. However in all cases, registration is about getting your name on a list to support some kind of future progression or action.
Apply has a much more general meaning. You can apply for a loan, and you may get an answer immediately or after some time. However it does not mean there is a "register" of names of people applying for the loan (each application may go into a different persons email box for individual consideration).
Because "apply" is so general, sometimes they can even be the same thing "Apply now to register your interest and we will contact you when it becomes available".