Okay, thanks, Cboldt.
Suffice to say that the term "martial law" is indefinite in its own right; is okay in casual conversation, but for substantive discussion it's better to go one layer below and inquire as to who is in charge of what, who is "making the laws," and where do the people turn for aid, police, and justice.
Complexity in the US is that the authority can be state, local, National Guard (under state control), etc. There are lots of permutations. Fortunately for us, the bias is to return control of civil liberty and civil order to the people and their elected government.