I'm sorry, but you have fallen for the usual misuse of an old term. You are defining the offset. Rake is the the complementary angle of the head tube angle, the angle made by the head tube compared to the vertical. Exactly the same definition applies to the masts of sailing vessels.
Trail, as I'm sure you know, is a different thing again, which can be derived if you know the rake, the offset, and the wheel radius.
Many people define the correctness of language as that which is used by the majority, in which case you are now correct and I am wrong. But that wouldn't be any good for pedants like me, would it?