* Anagram: This is the most common term when referring to two words with the same letters in a different order. For example, "listen" and "silent" are anagrams.
* Permutation: This term refers to any arrangement of objects (including letters), but doesn't specifically refer to words. So you could say that "listen" and "silent" are permutations of each other.
If the words are spelled the same but have different meanings, they are called homonyms. For example, "bear" (the animal) and "bear" (to carry).
Let me know if you have any other word puzzles!