What is the difference between a part of speech and a syntactic function / grammatical relation?

Solution 1:

Parts of speech are categories, their members sharing various properties. One of these properties is the functions that the members can perform. These functions are relations, and each should be capable of coming before of. For example, in faculty office, faculty is a dependent (more specifically a modifier) of office. It generally makes no sense to say that something is a noun of or verb of.

If we look at families. Man and woman are categories (like parts of speech). You can see a man or woman outside of a family situation and generally still put them in the right category based on various properties such as facial hair, breasts, size, voice, etc. One of the properties of men is that they can function as 'husband of', 'brother of', 'parent of'. Women can be distinguished from men partly in their inability to function as 'husband of' or 'brother of', but both men and women can function as 'parent of'.

Back to words, the members of the category of English nouns share a range of properties including (typically) inflecting for number and ability to function as 'subject of' or 'object of' verbs. Adjectives have other properties, like inflecting for grade (tall, taller, tallest) and ability to function as 'modifier of' nouns. Number and gradability are distinguishing characteristics, but functioning as 'modifier of' nouns is a shared characteristic. But we can still distinguish them based on their other characteristics. Only when the word takes on many characteristics of another category (like fun--traditionally a noun--being inflected funner and funnest) would we say that it actually now belongs (also) to that new category.

Solution 2:

For the time being, here is what Geoffrey Pullum has to say about this issue. This quote is taken from LEXICAL CATEGORIZATION IN ENGLISH DICTIONARIES AND TRADITIONAL GRAMMARS 2009:

Most of the deepest blunders in English grammar as traditionally presented over the past two or three centuries stem from a single long-standing confusion between (i) grammatical categories or word classes; (ii) syntactic functions or grammatical relations; and (iii) semantic and discourse-related notions.

It is surprising to see the tenacity of this confusion. It does not appear in other domains. People do not confuse butter knives with screwdrivers, even though occasionally someone who cannot find a screwdriver may use a butter knife to turn a screw. Yet in grammar people just cannot keep syntactically relevant categories or classes of words separate from the relational properties they have when used in particular constructions, and cannot keep either separate from meaning. They insist on trying to define the first of these in terms of the other two, and they have done so since the very earliest attempts to write grammars of English.

In short we need to be careful about confusing word categories and functions/grammatical relations. These two things are entirely different. A noun used as an adjunct or "adverbial" is still just a noun, not an adverb!

Solution 3:

Professor Lawler posted the following insightful and authoritative answer in non-searchable and ephemeral comments which I here reproduce verbatim as a Community Wiki answer to circumvent these infelicities:

Function is the wrong word; it’s pretty vague, even in linguistics. If you mean grammatical relation, however, that’s a term that refers to Subject, Direct Object, and Indirect Object; plus Oblique, which means “Everything Else”.

Parts of Speech (grammatical categories, not “functions” or relations) are syntactic (and occasionally morphological) categories that words can fall into. English has around 20 or so indispensable parts of speech, with lots of special-purpose cases. Most English words can fall into several categories. But there’s only 3 grammatical relations, plus Oblique.

And if you really do want to know what “grammatical function” means, you’ll hafta be specific about whose functional theory you’re referring to. I do use the word to refer to discernible affordances that certain structures offer, like the dozen or so syntactic rules (Extraposition, Right Dislocation, There-Insertion, etc.) that seem to have the function of moving heavy subject material to later in the sentence, to facilitate right-branching parse strategies.

But that’s not a technical term; there are all sorts of definition of “function” around, so you need some provenance.