"Frugal" and "prudent" both mean being cautious and economical in the use of resources.
"Prudent" also has the meaning of being cautious in other matters of self interest.
"It would be prudent not to tell your boss that you are looking for another job."
"Be prudent in what you say to the police..."
"Frugal" cannot be used in this sense.
"Frugal" can have negative connotations -
People (especially politicians, can be frugal with the truth. (A euphemism for saying: "they lie".)
"He was frugal with his hospitality." (A euphemism for saying he was not very hospitable, at all.)