Both Pohlig-Hellman and RSA perform encryption and decryption by exponentiation modulo some integer ($p$ prime for PH, $n$ composite for RSA). They both use a key $e$ as the exponent to encrypt a message. They both use the inverse element of key $e$ to decrypt. In both, the encryption key $e$ can be a randomly chosen integer coprime with $p-1=\phi(p)$ (for PH) or $\phi(n)$ (for RSA).
So what's the main difference between Pohlig-Hellman and RSA?
Note: The question has been edited for accuracy and more standard notations.