grammar is our fourth most used tag and grammaticality is our seventh most used tag. Yet, it would seem to me that they are used interchangeably. I cannot be sure since grammar does not have a tag wiki but, from a quick look at the two, it would seem they are.
Imagine that grammar is a circle. Everything inside the circle is grammatical and everything outside is not. For example, "Cat dream about chasing mice." is unambiguously and uncontroversially an ungrammatical sentence, and is thus outside the circle. “The cat dreams about chasing mice” is grammatical, and thus inside the circle. The tag grammaticality encompasses questions about where the boundary between grammatical and ungrammatical is. Here are good examples of questions about grammaticality:
- Is this usage of "aren't" proper English?
- Is "such a cooler" proper English?
- Which is correct — "I told you" or "I said you"?
Many questions tagged grammar have nothing to do with the question of whether or not something is grammatical. Instead, questions tagged grammar should be about how the grammar works—questions that ask “what is the structure of the inside of the circle of grammar?” rather than “where does the boundary of the circle of grammar lie?”. Here are some examples of such questions:
- 'I was using', 'I have used', 'I have been using', 'I had used' - what is the difference amongst these?
- Why call them infinite/finite verbs?
- Does the use of present perfect continuous with a time reference in the past imply an intention to finish, and if yes, how to avoid it?
These questions aren’t about whether something is grammatical or not—they are about different grammatical usages and how they can be used or what they mean.
Nevertheless, the grammar tag is overused. Many questioners who don’t really know the grammatical terminology specific to their question just tag their question grammar as a kind of default, ignorant of the terminology or topic that would be the best tag for their questions. Many such questions should be retagged grammaticality, while others should have neither tag, and would be better served by a more specific tag.
In my opinion they would be synonyms.