It is a fair thing to wonder, because the aquarium trade calls a lot of unrelated plants "moss". The surprise is which way it falls: Java moss really is a moss, while several of the other "mosses" in the hobby are nothing of the sort.
The real mosses
Java moss is a genuine true moss, Taxiphyllum barbieri (long sold under the old name Vesicularia dubyana, which caused years of confusion in the trade). It is a bryophyte, the same broad group as the moss on a wall, simply one that grows submerged. So are most of the other named aquarium mosses:
- Christmas moss (Vesicularia montagnei)
- Flame moss (Taxiphyllum "Flame")
- Weeping moss (Vesicularia ferriei)
- Taiwan moss (Taxiphyllum alternans)
- Phoenix moss (Fissidens fontanus)
- Willow moss (Fontinalis antipyretica)
All true mosses. If the label says one of these, you are growing the real thing.
The impostors
These are sold and used like mosses but belong to entirely different groups:
- Marimo "moss balls" (Aegagropila linnaei) are not moss and not even a plant in the usual sense. They are a green alga that happens to grow into a velvety sphere.
- Riccia or crystalwort (Riccia fluitans) is a liverwort, a bryophyte cousin of moss but a separate lineage.
- Monosolenium, often sold as "Pellia", is also a liverwort.
- Süsswassertang, sometimes called round pellia, is stranger still: it is the gametophyte stage of a fern, with no true leaves or stems at all.
Does it matter?
For day-to-day growing, not hugely; most behave like low-light, undemanding plants you attach to wood or rock. But it is worth knowing, because care differs at the edges, an alga and a fern are not going to respond to advice written for moss, and it saves you the embarrassment of insisting a marimo ball is a moss. For attaching and trimming the genuine aquarium mosses, see the aquarium mosses guide; for telling the land groups apart, see moss, lichen, liverwort or algae.