A family of Microsoft word processing software products for creating web, email, and print documents.
"Mark grammar errors as you type" happens during typing, just like "Check spelling as you type" marks spelling errors in the text as you type.
If you don't want a lot of grammatical suggestions as you type, clear the "Mark grammar errors as you type" option.
I find "Check spelling as you type" quite useful, though. Suggested errors get a squiggly underline and you can ignore them if they are not relevant or you can click them and see if you get any helpful suggestions.
"Check grammar with spelling" means that (possible) grammatical errors are marked when you run a manual spellcheck, for example by pressing F7 (of Fn+F7 on some keyboards).