Words where "not [word]" means more than a lack of

Sorry for the poor title.

Is there a name/category of words with the property that using "not" before them does not give a standard negation in a way similar to the given examples?

The two examples, which will help me make this question clear, are "recommended" and "supposed."

In both of these cases, "not recommended" seems to mean "recommended to not," while "not supposed" seems to mean "supposed to not."

To demonstrate:

"He did not jump across the pond."

What did he do? Well, whatever he did, it did not involve jumping across the pond.

"My professor did not recommend that I take both classes at once." This reads (to me) as though the professor gave positive advice against taking both classes. If "not recommended" meant a simple lack of recommendation, then this sentence would apply if I didn't speak to my professor, or if we simply had lunch together without discussing my classes.

If I say "we are not supposed to wear button up shirts to work", it reads as though it is against policy to wear button up shirts ("supposed to not") while if "not supposed" simply meant a lack of supposition, then this statement would be true as long as other types of shirts are allowed.

Are there other examples of this? Am I being clear?

Thank you.

(American, native English speaker, biology major here)

Maybe I'm missing something, but the original post seems to indicate that "not recommended" means the same as "prohibited" or, at least "recommended against." But that's not how I understand that construction. You may be faced with several options, & I haven't recommended any of them to you, but that doesn't mean I've advised you AGAINST them, either; I just didn't express a preference.

"My professor did not recommend..." just means(to me) that he didn't recommend it; not that he made a recommendation against it(although he MAY have done that, too)

Now, NOT SUPPOSED to....I get that; it means the same as "supposed to not." And so, in answer to your question...I don't know, & I'm hard-pressed to think of other examples like that.

I don’t think this is exactly what you’re looking for, but it seems similar enough to warrant mentioning:

Litotes: “An ironical understatement in which an affirmative is expressed by the negative of its contrary” (e.g. “You won’t be sorry.”)