Typekit offers fonts in a variety of types / suffixes:
And often these are combined. For example, https://typekit.com/fonts/kepler-std has a number of these.
Although I can make a good guess / visual check of these,
- What do each mean?
- When should each be used, and why?
"Display" is the one that I am particularly unclear on. And feel free to edit the question if there are types I have missed.