On Validation vs. Error Checking

Let me start with a couple of pedantic definitions; stay with me, the beef follows right afterwards.

Conventional wisdom says that validation is different from error checking.

Validation is performed at the boundaries of a system, to check the validity of incoming data, which is at all times presumed to be potentially invalid. When invalid data is detected, validation is supposed to reject it by returning an appropriate result, not throwing an exception. Validation is supposed to be always on, you cannot switch it off on release builds and only have it enabled on debug builds.

Error checking, on the other hand, is performed inside a system, checking against conditions that should never occur, to keep making sure that everything is working as intended. In the event that an error is encountered, the intent is to signal a catastrophic failure (throw an exception) instead of causing some result to be returned. Essentially, the term Error Checking is shorthand for Internal Error Checking.  It can be implemented using assertions, thus being active on the debug build only, and having a net cost of zero on the release build.

So far so good, right?