What is the difference between crucifixion and execution?

being crucified is being hung on a cross i.e like Jesus was, if you believe that. Execution is cutting someone's head off.

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Execution is the more general term. Crucifixion is one form of execution, among many others, including beheading. Crucifixion is not used anywhere in the world as a form of execution, at least as far as anyone knows. The Word 'execution' has meanins other than the taking of life, as used above.