In a recent test, the answer required was "mes parent aimeraient ce qu'on se marie" and the response "'voudraient'' was not accepted. Aren't either regularly used to mean "'would like?" I think technically the former is would like and the latter is would want, but that seems pretty subtle. For example, in ordering food "'Je voudrais avoir . . . .''
Yes, they largely mean the same thing. It's a question of how strictly the test is graded.
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