Is there a word for a "partial anagram"? By that I mean a word that can be made from some of the letters of another word, but not necessarily all of them (that would be a normal anagram). For example, HORSE contains the words ROSE and ORE among others. Is there a word for what ROSE and ORE are in relation to HORSE? Also, is there a website that will list all "partial anagrams", or whatever they're called, of a word? Thanks a lot.

I don't know the "official" answer to your question, but for words or phrases long enough to achieve respectability I would use near-anagram, partial anagram or quasi-anagram. For example, the rock group Camper Van Beethoven named oone of their recordings "Vampire Can Mating Oven," which is a near-anagram of their name. The smaller the word, the more trivial the near anagram becomes. It would hardly be worth mentioning that "I" is a partial anagram of "tasting" for example.

Cryptic crossword puzzles sometimes use near anagrams or contained words, with clues such as "found in The Senate" (5 letters) [these], or "Two stowed-away in, say, a 747?" [airplane --> airplane --> pair]. I'm not sure if there is any specific name for these contained words, or there is any distinction between words whose letters are already in order and those that are formed by rearranging.

"below the fold" (that is further down the 'menu' list of forum topics is beheading words which is similer, but not quite the same.

slow
low
ow!

the trick is to find a word that can have the first letter removed,and still be a word..
ow is barely a word--

but you get the idea.

we haven't played much with beheading words in a long time (for a while we exhausted our stock!)
we could start again.. (not that this answers your question.)

There are several anagram generation sites and even if none give partials, for a given letter string some give word sets, e.g., for DREAD the list would include AD RED. A search with "anagram solver" should find a good selection.

...including our own (well, Anu's, of course) Internet Anagram Server.

Wow, I've used the anagram generator on this site of course but I never realized that if I choose to "Print candidate word list only" in the advanced options, it will do exactly what I wanted in the first place. Thanks so much everyone!