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Kalpak is a generic Turkic hat in many forms, I would bet it's just a generic name for hat, even we have our versions and two words originating from it: kalpag and kalap. Now we use kalap for hard hats, like top hat or fedora and such. We use sapka for soft hats like beanie, from Latin cappa via South Slav šapka. But now I read kalap is from the German klappmütze so who knows.
Tubeteika seems a Central Asian/Muslim thing, although may have some connection with Jews there in Bukhara for example whose kippah looks similar I believe.