Words that have the same consonants in the same order are consonyms. For example, 'rues', 'ruse', 'rosy', and 'areas' are consonyms.
As far as I can find, this word is only used by those who like word games -- the search for consonyms can kill hours of time. You may make a distinction between 'normal' consonyms and mixed consonyms. Mixed consonyms have the same consonants in the same order, but in different groupings, for example, ethnic and thence.
The longest consonyms that I have been able to find are:
Common words:
- Incontrovertible and Incontrovertibly (16 letters)
- Incomprehensible and Incomprehensibly (16 letters)
Uncommon words:
- Diphenylaminechlorarsine and Diphenylaminechloroarsine (24 letters)
- Electroencephalographs and Electroencephalographies (24 letters)
- Microspectrophotometres and Microspectrophotometries (24 letters)
- Stereophotomicrographs and Stereophotomicrographies (24 letters)