It is a fair thing to wonder, because the aquarium trade calls a lot of unrelated plants "mosses". 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, one of the true mosses, the same broad group as the moss on a wall or a woodland floor, simply a species that happens to grow submerged. Like its land cousins it has tiny leaves only a cell or two thick, no true roots, and thread-like rhizoids that anchor it rather than feed it. 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.
- Suesswassertang, sometimes called round pellia, is stranger still: it is the gametophyte stage of a fern, with no true leaves or stems at all.
How to tell them apart at a glance
A true aquarium moss has recognisable tiny stems clothed in minute leaves, and it grips wood or rock with rhizoids while taking water in over its whole surface, exactly like its relatives on land. An alga such as marimo has no leaves or stems at all, only filaments of a single kind of cell wound into a ball. The liverworts, riccia and its kind, form flattened forking ribbons of tissue rather than leafy shoots. And the fern gametophyte sold as Suesswassertang is a lobed green sheet with nothing you could honestly call a leaf. A hand lens settles most arguments in seconds.
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. There are practical knock-ons, too: the true mosses spread from fragments and take happily to being tied or glued onto hardscape, whereas a marimo is rolled gently to keep its shape and never really attaches, and the liverworts have their own quirks of light and flow. Buy on the strength of the Latin name rather than the shop label, and you will always know what you are actually dealing with. 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.