What is the difference between a part-of-speech and a function? In other words:
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What is a part of speech. (e.g. noun)
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What is a grammatical function. (e.g. head, subject)
[read "grammatical relation" or possibly "syntactic role", if you prefer that terminology to "grammatical function" – see John Lawler's comments below]
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What is the difference?
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If we use a part of speech which is often used in one function, in a different function, does it change the part of speech of the word? For example, if we use a noun (let's say some nouny word that we can often observe functioning as a subject) as an adjunct, does it become an adverb?
Bounty Edit Note
These don't have to be addressed in different sections. One well illustrated paragraph which addresses the different concerns would be as welcome as a longer post with several parts!
I am hoping, though, that an answer to this question will, of course, give a description of what a grammatical function and part of speech actually are and not skip straight to the noun/adverb illustration!
I originally also asked about whether a noun used to modify another noun becomes an adjective as an example of a change of function. However, that has been covered in another question recently – though feel free to use it to illustrate your answer, if you'd like.
Motivation
Here's an example of why the question is interesting. In answers in rseponse to this question:
… several posts seem to indicate that a word's part of speech is determined by its function in a particular sentence. In other words, most answers on that page seem to argue that a part of speech is determined by how a particular word is being used. This is underlined in the top-voted and much linked-to answer:
… you will find that they have a category of adverb called a noun-adverb, meaning a noun used in a slot expecting an adverb, analogously to how a noun-adjective is a noun used in a slot expecting an adjective.
I wonder, however, whether functions and parts of speech can in fact be conflated in this way.
Best Answer
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.