How to distinguish a transposition cipher from a simple substitution cipher only given a ciphertext?
Think about what properties of the plaintext are preserved by the candidate ciphers. You want to look for those patterns. 

Transposition moves letters around but keeps their identity. Substituting keeps positioning but changes identity.

So, you can do a test for whether letter identity is preserved. 

The easiest is to do a frequency analysis: if your common letters (e, t, etc) are still common, you probably have a transposition. Of course if not, you are half way to breaking the substitution! 

A bonus test goes the other way: see whether position is preserved. A perfect transposition will shuffle the letters, so no pairs should come up more often than expected by chance. If there are any weirdly frequent letter pairs, those are evidence that you have a substitution cipher.