The difference between saturation and distortion is that saturation is often known as a more harmonic distortion and is increases the harmonic amplitudes by using a mix of distortion and compression to give the sound “warmth” and make the sound fuller. This dates back to when effects were a physical component going through a physical object in a circuitry whether it’d be a transistor or tape, often causing compression.

Distortion however is altering the shape of a waveform to give different tonalities. This can come in multiple forms including chromatic, clipping and even bit crushing. Where it can get confusing is how they both involve the amplitude increase of harmonics, hence the people who have never interacted with the physical components often losing the definition and having the 2 mixed up.

Source: https://youtu.be/vKsMjVvk3YE