Use assertions for internal logic checks within your code, and normal exceptions for error conditions outside your immediate code’s control.
Don’t forget that assertions can be turned on and off – if you care about things like argument validation, that should be explicit using exceptions. (You could, however, choose to perform argument validation on private methods using assertions, on the grounds that a violation at that point is due to an internal bug rather than an external error.)
Alternatively it’s entire reasonable (IMO) to use exceptions for everything. I personally don’t use assertions much at all, but it’s a matter of personal preference to some extent. (There can certainly be objective arguments for and against assertions, but it’s not sufficiently clear cut to remove preference altogether.)