A biological soil crust necessarily contains or consists of cryptogams, like algae, lichens, cyanobacteria, mosses. Structural and depositional crusts form as a result of processes forming soil structure or eolian/fluvial deposition of fine material, respectively (see http://www.fao.org/docrep/t1696e/t1696e10.htm).

This classification is based on different mechanisms of formation, so of course their development is based on different mechanisms. However, often these mechanisms occur simultaneously. For example, cryptogams grow faster when more water is available, at the same time fine material has a higher water holding capacity than coarse material, so biocrusts may preferably develop on physical crusts. Biocrusts are further known to capture fine material and, thus, contribute to the depositional crust formation.

You can recognize biocrusts in the field by their greenish appearance when wet, and by the presence of organic filaments. Also a magnifying glass helps to discover and to identify cryptogams. They are not "crunchy" when wet, but soft and somewhat flexible. I moisten the surface some 5 min or so before I start working with biocrusts in the field.

Geomorphology may give you some hints about physical crusts. For example, if you find a physical crust in a depression and you recognize paths of surface flow and erosion towards this depression, then you likely see a depositional crust. Micromorphology surely gives you more information (for example, stratification layers or particle orientation), but this is normally not done in the field.