What is the difference between electric and electrical and their usage?
For example, what is the difference between "electrical machine" and "electric machine"?
These two words have a large semantic overlap, but at the edges there are a few key differences.
So, in the case of "electric(al) machine" from your question, since you are talking about something that runs on electricity, the two words are essentially identical in meaning.
Here's a simple distinguishment which I hope will help:
"Electric" is used in front of a device or machine that runs on electricity. It is used when the object has been specified.
"Electrical" is used in a more general sense, as in referring to ambiguous nouns. (By ambiguous, I mean unspecified e.g. machine, appliance). "electrcal" is also used when the object is specified, but the object is not run on electricity, but is related to electricity i.e. Electrical engineer.
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Electric means "of, worked by, charged with, or producing electricity."
Electric cannot be always replaced with electrical; you don't say electrical guitar, or "the atmosphere was electrical" (if not to mean something else than the phrase using electric).