www.alphadictionary.com

Those are all names by which this month's full moon is known. Sap and Sugar I expect come from the spring rising of the sap in trees. Does anyone know whence the others?

According to what you, Slava, like to call the internot and supported by NASA and the Farmers' Almanac, all the terms you listed for referring to the first full moon in March were applied in various indigenous languages of North Eastern North America. (The sources cited below don't provide information on the specific languages.)
Crow Moon -- vocal activity of crows was thought to signal the end of winter (NASA)
Full Crust Moon -- above freezing day time temperatures and below freezing night time temperatures caused crust to form on the snow. (Farmers' Almanac)
Worm Moon -- Earth Worms appear on the surface of the soil as the soil warms up. (Farmers' Almanac)
As for Sap and Sugar, I expect your speculation is probably supported by the internot

Thanks for looking those up. It's interesting to see how people used to think of and relate to the weather.

I'm not really familiar with "Worm Moon", but it's clearly related to what I know as a "worm rain" -- a warm spring rain after which worms appear wriggling on the sidewalk, having been flooded out of their burrows. I have no idea where I first encountered this expression, but when it happens, it's pretty obvious.