"Эта женщина" is not a complete sentence and could be translated as "this woman" or even "the woman". "Эта женщина проиграла выборы" (This woman lost an election).
"Это женщина." is a separate sentence. You can say it when you are watching Eurovision and understand that Conchita Wurst is definitely not a man.
Eto is used for things whereas etot is used for people if I'm not wrong
You are wrong. In Russian you express the phrases this is, that is, these are, with the single form "это". We also use demonstrative adjectives to point to specific items in relation to ourselves. For example, to indicate a specific book that I want you to look at, I will point to the book and say "I like this book" (мне нравится эта книга). And you might reply, "I don't like that book" (мне та книга не нравится). The words "this" (это, эта, этот, эти) and "that" (то, та, тот, те) are demonstrative adjectives (i.e. they demonstrate or indicate nouns). As in other situations when a word is associated in some way with a noun, in Russian that word must agree with the noun in gender, number and case. This is the reason why in Russian there are four forms for the demonstrative adjective:
этот - masculine. Этот студент. / тот - тот студент
эта - feminine. Эта студентка. / та - та студентка
это - neuter. Это письмо. / то - то письмо
эти - plural. Эти газеты. / те - те газеты