[Linguistics Question] Does the 〜ている form result from a combination of the 〜て form and the verb いる?

e.g. Is 作っている (making, ongoing) the combination of 作る＋いる in the same way that 作って食べる (making and eating) is a combination of 作る＋食べる?

Context: I've always seen the 〜ています form listed as its own grammatical form. However it looks like any other 〜て verb connector. Is this special category just the streamlining of an old conjugation into a new form?

P.S. Sorry if this isn't the right place for this question, I didn't know where else to ask it!