To put it simply. hey are all Semitic people, but like Indo-Europeans (that includes iran and parts of india too) that describe most of Europe, its a language based cathegorization. Language tree so to speak. For semitic people, they can all in general find their ancestral roots back ibe thats similar to present day yemeni jews in general, as a language, and in parts ethnically too (but mainly as language, because semitic languages are afro-asiatic, so they include Ethopian amharic, Tigrinya etc). But mainly as a language group, which is a big part of what forms a culture and a people, even if the ethnic mix of it can be bit varied due to rich histories of conquest and intermingling tribes.
But ethnically the region is quite different, so it depends what part of the middle east or south central asia you referring to. Just look at the mix of country like Lebanon, you will get a headache trying to deduce ethnic makeup of it historically. And if you talk to the wrong Lebanese, he will slap you if you tell him he is descended from arab tribes