ReCaptcha Error "A public key for a different site was used to generate this CAPTCHA\n'"

[Norm Stephens]

I get this error on about 50 percent of websites I create, even if I
am using the same template and component etc. on two different sites
one will work and the other will give this error despite the keys
being definitely correct.

"The captcha wasn't entered correctly. reCAPTCHA said: 'Input error:
challenge: A public key for a different site was used to generate this
CAPTCHA\n'"

Having Googled the error there doesn't appear to be an obvious
solution.

Any ideas?