I understand that multi-effects like the Floor POD that have amp and cabinet simulation can be used instead of a "real" amp, but what kind of speaker are you supposed to play them through?

A regular guitar cabinet?

Some sort of loudspeaker?

I'm not sure.
I think a power amp and a cabinet is a popular combination.
I don't give a shit if you listen to me or not
if the pedal device has a line out for amp then you can run it to a standard amp just like a guitar and then say USB to PC for the software. Or you can buy the best sound card and computer speakers you can get and forget the amp.

not sure tho if that answers your question.

Preamp >> Power amp >> Cab

A processor is just the preamp part of a guitar head, except digital.

Hook it up to a power amp, and then out to a cab.
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