They both do that. Sometimes it looks like they're sipping off the top but they're really catching nymphs as they struggle just beneath the surface.
That's one of the "secrets" about fly fishing is that more trout are caught under the water's surface than on the top.
That's why semi-submerged flies like parachute flies and Klinkhammer flies do so well. The "parachute" at the top of the fly suspends the top half of the fly while the bottom half looks like an insect struggling to get out of its shuck and fly away.
Another good fly, especially for stocked trout, is called the AP Emerger (all purpose emerger). It's brown (same color as trout pellets) but also resembles a bug that's emerging and floating up towards the surface. You can float some of these beneath a float and gently pull it along or let the current do it, to give it a lifting motion as if it's coming to the surface.
Today I'm going to try fishing under a float with a mini soft bait, about an inch and a half long.
If you see bluegills around, it could be them, too. It's really cool when you see the trout breach the surface.
It's cool when you see them breach the surface. In California I've seen them do that when spiders were floating over the water, sailing on webs and by bees that were for some reasons flying around the water's surface.
Out here in New England I see trout (and smallmouth bass) jumping out of the water trying to catch dragonflies!