There are two subdivisions of homonym:
Homophone- words that sound the same, although they are spelt differently: rein, rain & reign
Homograph- words that are spelt the same, although they are different words- wind (moving air) and wind (a clock) look the same, but are pronounced differently.
There is a lot of confusion about the word "homonym".
In my opinion, there are three divisions of "homonym":
1. homophones: words spelled differently but pronounced the same way
b. lead (mineral)/led
c. read (past tense)/red
2. homographs: words spelled the same way, but pronounced differently
a. lead (verb)/lead (mineral)
b. bow (archery)/bow (ship)
c. wind (weather)/wind (watch)
3. homonyms/true homonyms/homomorphs: words spelled the same way and pronounced the same way, but that have different meanings and possibly origins.
a. bear (animal)/bear (verb)
b. bank (money)/bank (river)/bank (billiards)
c. swallow (bird)/swallow (ingest)
Some people would include different uses of the same word as homonyms: take (verb) and take (noun). I see no reason to include those. It is not unusual in English for a word to be a noun or a verb.