I always called this "chip". My UK friends called it "chip-and-pin" in 2012. But yeah, no idea what the technical or widely-accepted colloquial terms are.
> Not knowing for sure is why I never try, and just stick the card in the slot
Yeah, for some reason the UX for contactless is terrible. Sometimes something will show four evenly-spaced green lights (and sometimes they're blue--in any case, why does that mean "contactless"?) but often those lights don't appear until you attempt a tap-to-pay and then they might be delayed by several seconds. And even then, occasionally the hardware malfunctions and can't actually handle tap-to-pay. These hardware failures seemed to be way more common in the early days, but now almost everything does support tap-to-pay--you just often can't tell until you try which is just the dumbest thing ever.
> I think I've paid with my phone one time ever. For some reason I can't bring myself to trust it to work 100% of the time so I can leave my cards at home
I definitely do it as a last resort, but I've done it a few times (e.g., if I forget my wallet). Mostly on iOS I'm often trying to pay quickly and I try to activate the contactless payment but I'll end up turning my phone off or I'll try to bring up my card before my phone is close enough. The uncertainty always makes me feel way more anxious than it should and it's just less stress to use a card (cards also don't run out of batteries).
Having an Apple watch helps out a lot here. I can't do it on my phone either, but on my watch it is trivial.
Whenever "your transaction" begins at the register could be when you're eligible to present your payment to the terminal.
I generally pay with the apple watch if the store supports it (most seem to, nowadays). It is more convenient than reaching for the wallet since the thing is in my wrist anyway.
I always forget about contactless. I think all my cards can do it? Not knowing for sure is why I never try, and just stick the card in the slot, which always works.
I think I've paid with my phone one time ever. For some reason I can't bring myself to trust it to work 100% of the time so I can leave my cards at home, at which point I may as well just use a card since I have 'em anyway. I guess I could start carrying phone + cash as a backup and skip the cards, but that's even less convenient. I do activate the payment screen (iPhone) all the time by accident, though I couldn't tell you how.
(I'm not even that old...)