If one lexeme has a word form "goes", and another lexeme has a word form "goes", are those two word forms considered by linguists to be the same? In other words, is a word form defined solely by its grapheme sequence? Or is it also defined by its relation to a particular lexeme?
First of all, words (and therefore word forms) are not made of graphemes. They're made of phonemes; either the kind of phoneme spoken as sound (as in English) or the kind of phoneme gestured with the hands (as in American sign language). No human infant learns to speak with graphemes; we learn either with sounds, or with gestures. So human languages are shaped with sounds, or with gestures.
Writing is simply a technology to represent words in graphical form. By the time that writing arrives, the words were already there. Writing can represent words in infinitely varied ways (cf.). You could represent English words with Arabic or Devanagari or Tengwar characters if you wanted, or make up your own; it would still be the same words.
In general when studying language it pays off to distinguish language from writing, and to set writing aside unless you're dealing with writing-specific phenomena. Words and word forms exist in the domain of language, not of writing. If you want to understand words, first forget all about writing, and concentrate on the words themselves. You can later deal with the question of how they're conventionally graphed in a given culture.
Now let's consider the definition of “word form”. Technical terms can be tricky because they can have more specific meanings than the same terms would have in general language. For example, we refer casually to our "weight" in kilograms, but in the technical language of physics, that would be our "mass"; the "weight" is a different property, dependent on local gravity and measured in Newtons.
Similarly, no one would blame you for using "word form" to mean, in a casual way, "the form of a word". A word is an association between a sequence of phonemes (its form) and a meaning. So if you use the expression "word form" to mean "this particular sequence of phonemes", then sure, many words will share the same form. That's the common phenomenon of homophones. For example, "matches" in "I brought matches to make a fire" and in "he matches the criminal description" are the same form (the same sequence of phonemes), even though they're different words (different form/meaning pairs).
However, when linguists talk of "word forms", they're not just talking about forms of a word in a general way. Let's consult the Routledge Dictionary of Linguistics to see a technical definition:
The concretely realized grammatical form of a word in the context of a sentence. The word in the surface structure that corresponds to the lexeme as the (unalterable) abstract base unit of the lexicon is realized according to grammatical categories (such as tense, number, case, person, and so on) in altered ‘word forms,’ cf. picture, paint in Interesting pictures were painted. [emphases mine]
There are a number of things implicit in this definition:
- In some languages, some words can have multiple forms. Earlier I said that a word is a pairing of form and meaning. The notion of "word forms" complicate this definition a little bit; now there are several possible forms which we consider as belonging to "the same word", in some sense.
- These word forms can be conceptualized as "alterations" of a basic (or "citation") form. The most common alterations are affixes (walk→walked) and internal sound changes (sing→sang), though in some cases the forms are totally different (be→was).
- The criteria to consider these alternate forms "the same word" are grammatical; that is, they depend on the role of the word within the sentence. In English, for example, verbs will change for the past tense (though not for the future); so the past tense requires its own word form in this language.
- This is how we can tell that "was" is a word-form of "be"; because it fulfils the same grammatical function as "walked" or "sang" do in a similar context.
Under the technical definition of "word form", it makes no sense to say that "(the) matches" is the same word form as "(he) matches". They're the same form, but for different words; and a word-form is a grammatical variant of a word.
One way to understand the motivation for the technical definition is to consider what we use this concept of word-forms for. You might be doing some corpus analysis, for example. Suppose you want to calculate the frequencies of common verbs, something very useful for language learners. But you don't want to count all verb inflections as different items to learn (you don't want to count "learn" and "learning" and "learned" as different objects); you want to count the verbs as lexemes (because, after some instruction, learners can derive their own word forms according to context). So when you run your algorithm,
I'm matching and
he matches all should increase the occurrence counter of the verb
TO MATCH. But
the matches should not be counted, because it's a different word. It doesn't matter that it has the same surface form as the verb
matches; it's still a different word, so it's not a hit of the
matches word-form that belongs to
It can definitely happen. I have not example from English ready, but the Latin word form laudes can belong to two different lexemes: It can be the second person singular present tense subjunctive of laudare "to praise, to laud" or it can be the nominative or accusative plural of laus "praise, accolade".
Contrary to @jknappen I want to point out that modern linguistics tends to distinguish between representation and idea, for lack of a better word, so the difference between phoneme and grapheme is irrelevant. Going by a recent question for the definition of "word", there is no generally accepted answer. In information theory the smallest unit of exchange is a bit, in Computer Science, continuing the idea, a word is a fixed size bit sequence. In detail, there is a difference between phonemics and phonetics. Phonetically, @boiko's "matches" are not the same, the a in matchstick matches is longer - probably due to stress and place in sentence - though the broad phonemic descriptions are equivalent. So context is important, the word forms are not the same, the written description is broad and loose, and homophones are often enough related by etymology.
Edit: What a word-form exactly should be, depends on context, too. When searching for the term, I do see it used a lot in Computer Vision, so the written form does matter to some. There are results for developmental research on speech acquisition, too (check for example "Lexical exposure and word-form encoding in 1.5-year-olds" by Swingley et al. They use the more specific term "sound form" once but otherwise use "word form").