They can be used interchangeably in some cases such as "bu tip/bu tür örnekler yaygındır." meaning "these types of examples are common".
However, "tür" also has "species" meaning, and you cannot use "tip" in that case.
In this sentence, you might say "tip" instead of "tür" unless you are talking about species.
Looks like the origin of "cins" was Arabic "جنس," which originally meant "gender" or "race" (of people). This reminds me of English, where a writer can, for the sake of variety in his style, choose to go back and forth from several different names for the same concept, each one borrowed from another language.