Once you go looking, the aquarium trade offers a surprising spread of mosses, and they are not interchangeable. They differ in shape, speed, fuss and the look they give a scape, so it pays to know one from another before you tie it to your wood.
Java moss
The default, and rightly so. Nearly indestructible, tolerant of low light and a wide temperature range, fast to establish and forgiving of neglect. The trade-off is tidiness: left alone it grows shaggy and shapeless, so it rewards regular trimming. For a beginner, a shrimp tank or a low-tech setup, it is the obvious starting point.
Christmas and Taiwan moss
A step up in looks. Christmas moss grows in tiered, drooping fronds that genuinely resemble little fir branches, giving a denser, more deliberate texture than Java. Taiwan moss is similar, with neat layered growth. Both are a little slower and a little more demanding than Java, preferring decent light and gentle flow, and both look superb draped over wood.
Flame and weeping moss
These two earn their keep through their unusual habit. Flame moss grows upward in twisting, vertical columns that really do suggest green flames, useful for height and movement in a scape. Weeping moss does the opposite, trailing downward in soft curtains that look wonderful flowing off a branch or an overhang. Neither is difficult, though both reward stable conditions.
Phoenix moss, and choosing
Phoenix moss (a Fissidens) is a compact, slow, fern-like moss prized for foreground detail and for staying small and tidy. As a rough guide: pick Java for ease and shrimp, Christmas or Taiwan for a fuller draped look, flame for vertical accents, weeping for curtains, and phoenix for fine detailed work. They all attach and grow the same way, covered in aquarium mosses and propagating aquarium moss.