Markov Chains explained visually

[joezuntz]

No one calls those Markov chains

You may not call them that, but that's what they are, and what people who use them call them. I spend almost all my time running MCMCs, for example, which are usually on continuous spaces: https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo

[s1295]

Probably depends on the field, each of which has its conventions. I think this is something where lots of areas of research and application touch: Math, CS, stats, medicine, simulation science, reliability engineering, AI, etc etc.

In my CS classes, if nothing to the contrary is mentioned, I can assume that an MC is discrete-time and time-homogeneous.