This page is for people who don't yet know whether they're looking at moss or lichen. As of April 2021, the New Mexico Wildflowers app lists 154 species of moss and 251 species of lichen. I'm happy just to know the difference, and perhaps you will be too.
All of the photos on this page were taken in the Sandia Mountains, starting April 2021. Hover over images with your cursor to control them.
Mosses are non-flowering plants (they reproduce using spores). From a distance, moss looks like green velvet, and it's velvety to the touch. Given a chance, it often forms little green cushions. Most moss leaves are one cell thick, so they're very translucent when the sun is shining through them.
Lichens are not individual species but examples of symbiosis. The overall forms are provided by different species of fungus. Inside each lichen are algae (or in a few cases, cyanobacteria). The algae live among the filaments of the fungus, produce energy through photosynthesis, and share that energy with the fungus. The fungus provides a friendly environment for the algae, including by trapping moisture and nutrients for them. In some cases there's a third partner, a yeast. When lichens are brightly colored, that's usually due to the algae.
Remember that lichens are not individual organisms but colonies, and sometimes the outward growth of a colony is obvious. Or perhaps a piece will break off and land in a favorable place. That's handy because the fungus and the algae have been transplanted together.
When you see cup-like ascocarps emerge from the lichen, the fungus is reproducing by creating spores. Once a spore lands in a new home, the fungus needs to re-associate with an alga. Sounds like a challenge.
You may think that my photo of a tree trunk (above) shows moss and lichens. Not so. Lichens come in multiple forms, including the bushy ("fruticose") and leaf-like ("foliose") forms on the trunk. When lichens form on a live tree, they're not being parasites; instead they're using the tree as an apartment building.
In the uppermost Sandias you may encounter long, hairy lichens that you're tempted to call Spanish moss. In fact, these lichens are unrelated to Spanish moss, which is a plant of the U.S. Southeast. The correct name is Old Man's Beard (Usnea).