I don't think my definition is different from the common one. I agree that undefined behavior is behavior that the spec for the language says is undefined.
Pretty much every language has some undefined behavior. That undefined behavior can be invoked intentionally, or because of bugs.
C has a lot of undefined behaviors. Even simple addition can result in an undefined behavior because int overflow is undefined. Any C program that takes numbers as input (via the shell, or FFI, or whatever) and adds them together can exhibit undefined behavior. Null pointer dereferences are also undefined, and pretty much any C program of reasonable complexity can encounter those, in the form of bugs.
A bug in hardware can also cause these undefined behaviors to be invoked -- for example, a friend of mine who does embedded programming had some null pointer dereferences or something like that because the hardware did not set a value when he told it to set the value. Null pointer dereferences are undefined, and if they happen because of hardware bugs, that is a case of hardware causing undefined behaviors to happen. It would not be reasonable to say they were not undefined behavior simply because they were caused by hardware instead of programmer error. The fact that it happened at all is what matters, not what caused it.
Even if a language does not have any undefined behaviors whatsoever, that's not the end of it. If a program in that language interacts with other programs that do have undefined behavior, such as C programs, it could potentially trigger or be affected by undefined behaviors in those other programs. If that happens, it's not reasonable to say that it was not undefined behavior simply because it happened in a piece of code in a different language. (So, if the result of running a Python program is affected by undefined behavior in the C implementation of Python, that program has undefined behavior -- even if the Python code does not. The undefined behavior is C's, not Python's -- but it happens because of running the Python code, which caused the C code to run.)
In other words, any invocation of code that causes undefined behavior to happen -- whether it is intentional, or caused by a software bug, or even caused by a hardware bug -- counts.