"distinct languages" is a perfectly correct and usable phrase in written English.
For example, you could say, "The country is home to more than 200 distinct languages."
About 30 distinct languages and dialects have been identified.
India is an extremely diverse country with many distinct languages, cultures and religious communities.
Roughly 200 separate groups speaking distinct languages live around the Sepik River.
The original, single Slavonic tongue had splintered into distinct languages and dialects.
Several hundred distinct languages are spoken in the Pacific Islands; these are mostly Austronesian in origin.
All of these are considered to be distinct languages and not simply dialects.
Besides, English and A.S.L. are unrelated and different in terms of vocabulary, grammar and semantics; they are two distinct languages.
While they have distinct languages, both were part of the Austro-Hungarian Empire and share a Roman Catholic religious identity.
For the same reasons, dialect divisions that earlier would have widened into distinct languages are now unlikely to do so.
However, this number does not distinguish among many speech communities that could legitimately be considered distinct languages.
Two distinct languages are known, labeled A (East Tocharian, or Turfanian) and B (West Tocharian, or Kuchean).
