Timing attacks assumes that an attacker knows how long a particular encryption operation takes. I like to think of these attacks as biological. There are some things you just can't learn about an organism by taking it apart. Sometimes you have to look at the inputs and outputs. Call them side-channel attacks.
Normal attacks look at the plaintext and the ciphertext and attempt to recover the key.
These attacks don't necessarily generalize. A fault-analysis attack just isn't possible against an implementation that doesn't permit an attacker to create and exploit the required faults. But these attacks can be much more powerful. Some researchers have claimed that this is cheating. True, but in real-world systems, attackers cheat.