No, they don't--not those words, not in the case of Netanyahu.

I pretty much agree with your thesis here overall--we spend way too much time arguing over definitions, way too little time arguing over content. It doesn't matter too much whether you call something a genocide or a kerfuffle as long as you (and others) react appropriately for what is actually happening.

The problem is that people will simplify from what is actually happening to a word or phrase, then reason from the phrase instead of the reality. In that case, the reasoning is going to be wrong because it's oversimplified, but it will be even more wrong if the word or phrase is a poor fit to begin with. Ideally, people would go based on reality; but if we accept that, alas, they're going to oversimplify and reason from a word, then it does actually matter quite a lot that the word is a fairly good fit.

When Netanyahu compares Hamas to Amalek--not Gaza! (check your reference! I did!)--we don't all understand what those words mean. Maybe intentionally so.

The reason we can't understand is because Netanyahu did go out of his way to say Hamas, but at that point the parallel is bad enough so that we have two competing hypotheses which are difficult to conclusively distinguish (and, indeed, we can add additional hypotheses that involve Netanyahu trying to have both meanings depending on who is listening):

(1) Netanyahu is telling us that Hamas are the Amalekites and the Palestinian citizens are their ox and sheep, so all Gaza and Gazans get destroyed--but then why not simply say Gazans are the Amalekites?, or

(2) Netanyahu is telling us that Hamas are the Amalekites and need to be destroyed utterly, and it extends to Hamas-associated stuff like tunnels (ox and sheep = tunnels), but non-Hamas Gazans are not included except inasmuch as they're in the way--but then why use such a gruesome parallel that involves actual genocide?

(There are answers to both "but then why" questions--and the existence of answers to both makes the "he meant for both interpretations to be heard" hypothesis more likely.)

Either way, there are things to criticize about the parallel (e.g. Bibi is tacitly yet strongly encouraging war crimes either way!!!). But this is almost a canonical example of something where we can't understand what the words entail.