Bryophytes consist of mosses, liverworts, and hornworts. They are non-vascular and lack true leaves. There are two general groups of mosses defined by their growth forms: (1) cushion mosses (acrocarps) are having stems that are single, separate, and; (2) carpet mosses (pleurocarps) that are more branched and sprawling.
General group names aren’t always as useful since cushion mosses grow tightly packed together like tufts of carpet, and carpet mosses grow intertwined together to form mats (confused yet?). As another example of common name misnomers, other things that are not mosses: Spanish Moss (a flowering plant), Reindeer Moss (a lichen), and Clubmosses (a fern ally).
Liverworts have their main leaves in two ranks or rows and often a third row of reduced underleaves. Hornworts may get their name for their spore-producing stage.
The best way to learn your bryophytes and how they are different or similar to other cryptogams is to learn about their reproduction. The Ohio Moss & Lichen Association (OMLA) has a great Bryophytes 101 page to learn more about them.
A guide for over 600 moss species using only a hand lens in the field.
Karl B. McKnight, J. R. Rohrer, K. McKnight Ward, and W. J. Perdrizet. 2013. Common Mosses of The Northeast and Appalachians. Princeton, NJ: Princeton University Press.
A snapshot guide that helps you to learn moss Genera characteristics more so than individual species.
Munch, S. 2006. Outstanding Mosses & Liverworts of Pennsylvania & Nearby States. Sunbury Press.
An oldie, but I like the simplified line drawings.
Conrad, H. S. 1956. How to Know The Mosses and Liverworts. Dubuque, Iowa: WM. C. Brown Company Publishers.