Estimate is generally when you have some sort of knowledge on the topic, and some kind of solid mathematics, research, or science behind it.
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Guesstimate is used, and generally when you have an even more vague idea of the thing or have little knowledge on it, or the research to back it up is not there yet.

I say scotless instead of scot-free

England, for example, at one time tried to make sure Scotland would be Scot-free

At my previous employer it was all the rage to say “take a SWAG at it.” I had to ask several people who used the term regularly before find someone who knew what it actually meant: Scientific Wild-Ass Guess

I'll do you one better - hypothesizimate