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"they had at last confirmed the existence of the elusive Higgs boson"

Last I heard they have not yet found the Higgs boson, they found something that is LIKE the Higgs boson. Is this not correct?

It's probably the Higgs. There are some decay paths that have not yet been observed, some because they haven't analyzed that data yet, and at least one that just doesn't appear to happen as often as predicted (very interesting). But it's acting almost exactly as the Higgs should act, so while it's not absolutely sure, there's no real reason to think that it's not the Higgs.
Just out of curiosity, is "discover" really the correct terminology here? Didn't these scientists, more correctly, observe the Higgs? Not only that, but didn't they also observe phenomena that coincides with the existence of the Higgs without actual observation?

I'm not arguing with the title, simply curious as to what the correct terminology is for when something is previously hypothesized as being in existence.

They didn't know if it existed or not. Now they know it exists. Most high-energy particle physics is done by analyzing decay products of short-lived particles, so I don't begrudge them that.
It was covered, and now somehow unveiled. They didn't invent it though.
Out of curiosity: Even if they discover higgs boson, is there any chance for standard model to be changed again later on? (when somehow we discover yet another component)
> Even if they discover higgs boson, is there any chance for standard model to be changed again later on?

Yes.

No matter what they discover that is consistent with the standard model, there's always a chance that a later discovery will invalidate the standard model.

One difference between science and math is that you can prove things correct in math. In science, you can only prove things incorrect.