In general, unless a word is listed in a dictionary in a hyphenated form (in which case it's a hyphenated word), what you are looking at is just two words that have been hyphenated.
For instance, there is no single word as fifteen-legged:
It was a fifteen-legged centipede.
The centipede had fifteen legs.
In the first sentence, the two words are joined by a hyphen because they form a compound adjective.
Logically, if fifteen-legged were an actual word, then so too should be all of the other numerical combinations—but that's neither practical nor, ultimately, possible if expanded to every iteration. (Note, though, that two-legged, three-legged, and four-legged seem to have had enough popular usage that they've found their way into some dictionaries.)
However, high-pitched has become an actual word:
having a high pitch · a high-pitched voice
Although high-pitched is serving the same function as fifteen-legged, high-pitched is a hyphenated adjective, while the hyphen-combined words fifteen and legged form a compound adjective.