In this case, though, an automatic transmission is - for all intents and purposes - a transmission that does not require the driver to handle shifting at all. The DCT fits in this category.

AT is "the car changes gears".

Sometimes a distinction is made between AMT and others because AMT is kinda shit, but both DCT and torque are AT.

Also modern torque converters have lock-up clutches, meaning once they've switched gear they've got the same direct-coupling efficiency as a DCT. The ZF8 mentioned by Klonoar is a torque converter.

Ha, you're right! I don't have the energy to go edit my parent comment but hopefully it's clear (or at least, now) that I meant old school vs modern AT transmissions.

Thanks for the correction!