What is the difference between constant and consistent?

These words have various meanings, as your dictionary will tell you.

Very, very broadly, here's my first reaction to them with no context.

constant - all the time.

eg There was a constant noise in the classroom all day.

consistent - not varying

eg His behaviour in class for a year was consistent. He was a nuisance every day.

'constant' is something stable or permanent while 'consistent' may refer to density, something like 'dense' or'solid';
anyway a dictionary should help...
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 Clive's reply was promoted to an answer.