I'm doing my morning 'catch up' but in case no one has addressed this:
Jelly - Juice, pectin, sugar, no fruit bits, translucent. Cooked before bottling/canning
Jam -Juice, fruit bits or small chunks, pectin, & added sugar, thick and 'sticky'. Cooked before bottling/canning
'Spread' - fruit puree, sometimes with small bits, no added sugar. Usually uses fruit juice as sweetener. Usually not cooked before bottling/canning.
PB&J can be with jelly, jam, or spread but it's still called a PB&J. Not my fav, but mostly because I don't like PB very much. PB, butter, & honey is delicious, especially on toast.
PS someone mentioned 'preserves'. That can be jam, jelly, chutney, veggies, etc. Pretty much anything that's pickled, salted, or boiled with sugar then 'preserved' by bottling or canning to prevent spoilage.