I’m not a linguist, but here’s how I see it: They are analogous expressions, but as I mentioned, «estar» is not considered an auxiliary verb in Spanish conjugation. You only have «haber», while English has “to be”, “to have” and “to do”. So, technically, in English the expression is “conjugated form of auxiliary to be + gerund” while in Spanish it is defined as a paraphrasis composed of “conjugated form of to be + gerund”. Tomayto, tomahto.
To be clear, this is just a difference in the traditional grammatical terminology for each language. Linguistically speaking neither English nor Spanish has any such thing as a "present continuous tense".
Of course, the exact linguistic notion of "tense" is not particularly relevant to most people learning a language. I'm not objecting to its broader use in the context of language learning.
