Nope. There is nothing fuzzy about pushing and pulling. They have absolutely nothing to do with exposure. They simply refer to lowering/raising film contrast during development by varying temperature or time. You can even push unexposed film: get it fresh from B&H, don't bother with cameras, load it right away into a Paterson tank and develop in stock D76 for 24 hours for an extreme push!
It's very simple. The "fuzziness" comes from Youtube.
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