It is not clear what "caught" mean. The rough equivalent of the Python code:

try:
    ...
except AttributeError:
    raises TypeError

is the C code:

...
if (result == NULL) {
    if (PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_SetNone(PyExc_TypeError);
    }
    return NULL;
}

Is an AttributeError exception caught here?

The precise condition inside _PyErr_SetObject is if _PyErr_GetTopmostException returns a non-None value:

So some other ways to say this (without reference to C functions) are (1) if there's an "active exception" (the wording in do_raise()'s RuntimeError message), (2) if an exception is currently being handled (anywhere on the stack), or (3) if sys.exc_info() would return an exception.

sys.exc_info()'s documentation
https://docs.python.org/3/library/sys.html#sys.exc_info

Do you have a preference?

I would say "active exception". Could you make that change? In that case, I can merge this PR unless @serhiy-storchaka has further comments.

Is the term "active exception" explained anywhere? Should not a link be added?

The term used by the PyErr_Occurred docs is "the error indicator is set".

LGTM. @serhiy-storchaka Can you review it?

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