My mother used to collect Victorian and Mission style antique furniture.
When you say “daybed”, I think of an early version of a sleeper sofa, a mechanical contraption that sleeps one–sort of. A daybed (the pullout kind) is a sleeper sofa that says “this isn’t for serious sleeping”. I’m not sure exactly when they were invented, but I have the impression it was back in the early part of the 20th century, and it was considered tacky back then to have “sleeping arrangements” in the living room. Respectable middle-class folks were expected to “sleep” in “sleeping rooms”, i.e. the bedrooms. Only “po folks” had people sleeping in the living room.
Hence, the “daybed”, a sleeper sofa with a respectable name. It’s theoretically, officially, for “resting”, not for “sleeping”.
Like a chaise. And like a chaise, it’s not really designed for serious sleeping, being just a teensy bit too small for comfort.
But, see, that’s okay, since it’s not for “sleeping” anyway–it’s for “resting”.
Other than that, for the modern version, what Opal said.