Once bitten, twice shy / fool me

what dose "once bitten, twice shy" mean exatly?

If you fall in love with someone and that someone rejects you--"once bitten"--you may be very, very reluctant--"twice shy"--to let yourself fall in love again.

It's sometimes rendered "once burned, twice shy." Same meaning.

Almost the same as 'Fool me once, shame on you. Fool me twice, shame on me?"

SR