Is there any grammatical or semantic difference between the phrases:
"Are you coming to get me?"—used to imply the question of whether that particular person is coming to get whoever.
And this phrase:
"Are you coming to get me"—implying that the person is late or has been expected earlier.
I'm curious as to whether these sentences have only semantic differences or if there is a difference in the case or tense—or something like that—used.
You're asking whether the sentence is ambiguous, and whether the ambiguity is in pragmatics or semantics.
Pragmatics is a subfield of linguistics and semiotics that studies the ways in which context contributes to meaning. Pragmatics encompasses speech act theory, conversational implicature, talk in interaction and other approaches to language behavior in philosophy, sociology, linguistics and anthropology. Unlike semantics, which examines meaning that is conventional or "coded" in a given language, pragmatics studies how the transmission of meaning depends not only on structural and linguistic knowledge (e.g., grammar, lexicon, etc.) of the speaker and listener, but also on the context of the utterance, any pre-existing knowledge about those involved, the inferred intent of the speaker, and other factors. In this respect, pragmatics explains how language users are able to overcome apparent ambiguity, since meaning relies on the manner, place, time etc. of an utterance.
The ability to understand another speaker's intended meaning is called pragmatic competence. - wikipedia
Since your sentence is identical in both instances, syntax and grammar are the same. The semantics can be different, depending particularly on the meaning of get (get=fetch or get=assail). However, even if we take get to mean fetch as your question implies, the pragmatics are different.
If you don't know who is going to fetch you, then your first interpretation makes sense, with a stress on the word you in the sentence. If your enquiry is about whether the person is coming to get you at all, the stress is on are or coming. Stressing other words leads to other interpretations.
So to answer your question, yes, it's ambiguous, and the ambiguity lies in semantics and pragmatics.
Depends what one means by grammar. The grammar books of my schooldays would cite a sentence like "Are you coming to get me?" as an instance of stress or accent.
I've read somewhere that the early British phonetics buffs argued that accent was somehow grammatical, but our writing systems were so deficient that we could hardly recognize or comprehend its system. (Eventually such disciplines might coalesce, and a more abstract, but cleaner and better grammar would emerge.) Older books file accent with elocution, half of the art of which consisted in attempting to correctly infer probable accents in texts (where no accents were recorded) that would be otherwise obscure or unintelligible.
In 2016, what discipline claims the territory of accent? On this page Lawrence plants flags for linguistic pragmatics and semantics. Supposing these to be on very firm ground, this knowledge should naturally trickle down to improve our society. In 2016 we have sophisticated artificial languages created for fiction and TV shows, but our national rulers are not notably more eloquent, and a general unintended obscurity fuddles forth.
Maybe in 3016...
I don't think there's any grammatical or semantic difference between the two. The difference is in the emphasis placed on different words in the sentence. And the context largely determines where this emphasis would go.
When a person says this, it is clear from the tone and from what's happening what the speaker means. A person may be at an airport waiting for a friend. After five minutes, he calls his friend and asks the first question to clarify their plans. After an hour, he calls and asks the second question to ask his friend what's taking so long. In text, e.g., in a book, the meaning becomes clear after the circumstances have been laid out.
And emphasis can be placed on any part of the sentence.
Are you coming to get me?
Are you coming to get me?
"Are YOU coming to get me?" suggests that I expect someone will get me, but I'm not sure if it's you.
"Are you coming to GET me?" suggests that I expect you to come closer to me, but I don't expect you to come all the way to pick me up.
"ARE you coming to get me?" suggests that I expect(ed) you to get me, but I'm now trying to clarify if that's still true.
[Sorry, I realized after re-reading your question that it requires a technical answer which my reply above does not address.]
Surely that depends on which particular word is stressed, with each combination having different connotations.
Stressing the word get could imply a variety of different meanings from the innocuous (and presumably intended) meaning of simply picking someone up through to the more sinister get (as in, catch/harm/capture).
However, leaving the word get alone and stressing the word you simply implies, to me, that there are other potential getters.
To me, context, stress and vocal inflections are key.
