Not really. "jellyfish" is just a common catch-all for many
species from several different classes. If ya stick to
scientific nomenclature, confusion is reduced (but not
eliminated). When ya argue that palms are not trees, or spiders
are not bugs, ya get into trouble. Even the Florida Horse Conch
is not a conch, and the poor bastard gets stuck into a different
genus every few years.

You are correct that Physalia physalis (which we call the
man-o-war jelly) is not a "true jelly" which is a goofy name for
solo medusae.

They are far more common in the summer and, because the float
(which we call a sail) moves them with wind as well as current,
they are most frequently seen when the wind is out of the east.

They provide great amusement, as tourists love to prod them with
their toes on the beach.

All cnidaria, btw, have nematocysts. Some, like most coral or
moon jellies, are ineffective versus humans. Others, like
stinging hydroids or man-o-wars, are very effective.

m