If you mean the text input box, there is no standard word in Korean. In English, it is called "text input field, text input box" In Korean, it is called "입력칸, 입력란, 입력창, 텍스트 (입력) 필드, 입력 필드"

Other than "cursor" or "caret", you might call it: - character entry location = 글자(가) 입력되는 자리 / 텍스트 입력될 자리 [or 부분(part) / 위치(location)] - character entry space = 글자 입력 칸. (칸 means small segmented space, or sometimes a whole line)

Ah I got what you are asking. Umm.. I guess there is no fixed term for it but you may say words like '입력창', or '입력하는 창', or '입력하는 칸' to express it. Especially for the search engine, it would be '검색창'.

I think because "caret" & "text-cursor" sounds too simple. I'm looking for the name of the whole thing, not the line that shows you where you're typing, if that makes any sense. Like if you take away the blinking vertical line (the text-cursor) that indicates where the next letter will appear, what's the name of the field you write in? I have this glitch issue with my cell phone keyboard sometimes where that whole field disappears behind the keyboard in certain apps, yet I can still type (I can't see what I'm typing though). So I've wanted to try explaining that in Korean.

It would be 커서 or "키보드 커서". Why do you think that "text-cursor" or "caret" are not the term you are looking for?