This post gets a ludicrous number of hits for something that includes a definition of something that isn't really a proper technical term at all.
A "phoneme" is a discrete unit of sound as used in speech. It is therefore smaller than a syllable. The sound associated in English with both the letter "s" (as in 'less') and the softened letter "c" (as in 'space') is a phoneme.
A homophoneme, if it existed, would therefore be a single sound that can be written in more than one way. The sibilant sound in both "less" and "space" is the same phoneme, hence these are homophonemic.
My original post is much more about spelling than about sounds. Homophones are words that are spelt differently but sound identical, like your, you're, yore or their, there, they're. In both of these examples in UK English the single syllable sound is composed of two phonemes and in US English of three phonemes (arguably, some US dialects differentiate "there" and "they're"). It is silly to spell these things differently, but it is convention to do so, so we do.
Languages that use symbols to represent syllables don't (typically) have this sort of problem.
Words that are wrote differently but said the same. There aren't all that many of them, and most of them are short. One syllabic.
They don't confuse us when we say them aloud, so why do we write them different?
There is an honest answer, and a dishonest one.
The honest answer is short, incomplete, and not very satisfying, although it is, as forestated, honest:
Convention means that we have all agreed, and that latecomers agree that they also agree, as they arrive, that we will all do it the same way, and having thus agreed, he will cause consternation who chooses not to agree with, and follow, said convention.
(A little aside on consternation. Normally one person can't be consternated, or consterned - neither participle really exists, but consternation is a description for groups only - rather like convention and for similar reasons. I like to coopt consternation for the feeling of confusion that arises from an idea being expressed in a form of words that is sufficiently exotic, eccentric our outlandish (all of which mean the same thing, and are therefore heterophonic homologs) that it causes a moment's hesitation whose wellspring is the confounding of "did I hear that right", "did s'he really say that", "is that what s'he meant", "is s'he trying to confuse me" "?" (The question mark is for all four. It looks wierd in the middle of a sentence.)
Convention is handy because it means that we don't have to provide a justification for something that we just feel suits us. The last phrase is my test for a convention.
The dishonest answer is that we spell them differentwise to avoid confusion. Now I may have already mentioned that we aren't confused when we're speaking aloud. The dishonest answerer goes on to say that yes, well, but, when you speak aloud there are all sorts of additional clues as to the meaning of words, such as body language, intonation, facial expression.
Do you think you need these additional clues in order to differentiate "there" from "their" or "one" from "won" ?
"Their one won there."
"There won one their."
Wierdly, the first is a "correct" sentence, the second is nonsense, but if you say them aloud they mean the same thing.
In French, noone ever confuses a bucket, a seal (wax) , an idiot and a jump, even though seau, sceau, sot and saut are all nouns! (And pronounced exactly the same, regardless of what some linguists may claim.)
The truth* is that it is a convention, and while unnecessary, it is sometimes handy - like describing in print the difference in meaning between "their" and "there", the reader knows which one you are referring to.
*For a given value of quince jelly