"Moss" gets blamed for a lot of green that is not moss at all. Telling them apart takes only a close look, and it matters because they want different things and respond differently to treatment.
True moss
A soft, leafy plant with tiny leaves arranged around a stem, forming cushions or carpets, very often with fine stalks carrying capsules held above the green. If you can see little leafy shoots and stalked capsules, it is a moss.
Liverwort
Either flat and ribbon-like, pressed close to the surface in branching green lobes (the thallose kind), or leafy and very low-growing. No upright leafy stems like a moss, and the spore capsules, when present, are quite different. Liverworts favour really wet, often disturbed ground, such as the surface of pot compost.
Lichen
Not a plant at all, but a partnership of a fungus and an alga living as one. Lichens are usually crusty, leafy or shrubby in texture and often grey, white, yellow or orange rather than fresh green. They feel dry and tough, not soft, and grow very slowly on bark, stone and roofs. Reindeer "moss" is in fact a lichen.
Algae
A formless green film or slime with no leaves, stems or structure at all, on damp paving, timber, glass and pots. If you can smear it and there is nothing leafy to it, it is algae.
Clubmosses
These look mossy but are larger, with tougher, scaly stems, and belong to an ancient vascular group quite separate from the true mosses. Mostly you meet them on heath and hill rather than in the garden.
A quick field test
Faced with a patch of green and unsure what it is, a few seconds of looking usually settles it. Is it soft and leafy, made of tiny shoots you could tease apart, often with fine stalks standing above it? That is moss. Is it flat, lobed and pressed to the surface with no upright shoots? Liverwort. Is it crusty, leathery or shrubby, dry to the touch and a colour other than fresh green? Lichen. Is it a structureless film or slime you can wipe away in one smear? Algae. A hand lens turns these hunches into certainties, and once you have checked a dozen patches the answer comes at a glance.
Why the distinction is worth making
It is not mere pedantry. The four groups want different conditions and respond differently to whatever you do about them, so misidentifying the green is the first step to mistreating it. Algae signals a surface that is simply too wet and shaded and will wipe off; lichen is slow-growing and harmless and generally best left; liverwort on pot compost points to overwatering; and moss, depending on where it is, may be a welcome carpet or a slip hazard to manage. Knowing which you have tells you whether to leave it, encourage it or clear it.