Heterograph
Heterographs are words that sound the same, but are spelled differently and have different meanings. They are also known as homophonic heterographs. English example sets are "there, their, and they're"; "your, you're, and yore", "its and it's"; and "here and hear".
For a full discussion of similar sets of words and their relationships, see homophone and heterography and homography.
Heterographs are an especially problematic case, in that spelling errors (in a word-processed or emailed document) due to the typist choosing the wrong member of a heterograph set will persist into the final document, even after spell-checking. This is because heterographs cannot be caught by a simple spell checker, which only inspects the word itself (i.e., which is correct in some contexts) and not the context it is in (which may indicate the need for a different spelling).