The ESTA form explicitly includes "withdrawn your application for admission", as part of the refused admission question.

So it's basically the same, and you will have to apply for a proper visa.

What's an ESTA form? I've never encountered one as a Canadian.

Canadian citizens are exempt but this is the program that allows non-visa travel to nationals of certain countries https://esta.cbp.dhs.gov/

I don’t know what the policy is, but you can be denied entry for any reason