No, there are many types of distortion. Any time the output signal doesn't completely follow the input it is said to be distorted. It's pretty much impossible to build an analog circuit with active components which does not distort the signal in someway as it passes through. Based on that, as you can see, sheering off the tops of peaks is definitely distortion.
There are two classifications of harmonic distortion. Even-order and odd-order. Clipping causes odd-order harmonics, which sound harsh. But tube amplifiers primarily have even-order, which is almost pleasing to the ear, it causes the sound to seem "warm" or "fat". One can have 5% even-order distortion and still think things sound great.
As John said, the usual way one measures an amp is to drive it until the clipping is contributing 0.3% to the THD. At that point the amp is giving all its truly usable power. Though there are still different measurements here. Some use a 1k sine wave, others broadband (20 to 20k) noise, sometimes one channel driven, sometimes all. The FTC says (not the FCC, the Federal Trade Commission came in to stop the deceptive advertising), all channels driven with broadband noise.
