I know nothing about this but JumpCrisscross seems to use "political" to mean "has donated large sums of money" while your use of "political" is more like.. someone who does politics.

I think they're using it in a technical sense that's idiosyncratic to America: "career" members of the Foreign Service Corps, versus "political" appointees that can be directly appointed at higher ranks, but at the pleasure of the (in turn politically-appointed) secretary.

The first might have joined the Foreign Service and worked their way up; the second might have had a career elsewhere (not necessarily in political office), get invited to work for an administration, and then leave once there's a change in power.