200% faster means 3x the nominal speed:

You're adding speed ("going faster").

You're adding a 200% of speed, which is twice the nominal speed (the 100%). Given the nominal speed is 1x and you're adding 2x, you end with triple the magnitude of the original nominal speed.

You've dodged the question mark. What does 50% faster mean? What does 67% faster mean? What does 75% faster mean?

I'm using the exact same terminology, so splitting hairs on phrasing isn't going to work for me.

Something crawls along at 1 m/s.

After some clever engineering, it now runs 50% faster. Its speed is now 100% (the original rate) + 50% (improvement) = 150% of 1 m/s = 1.5 * 1 m/s = 1.5 m/s

50% faster means original speed plus 50%, or 1.5x

As sibling comments said, 50% faster means adding 50% of the nominal speed, so it's 1.5x the original magnitude.

It would be nice if this were the universal meaning of this phrasing but people do use it to mean both "twice as fast" (2x) and "faster by double the original speed" (3x).

People will rail about them using it wrong but it's pretty useless when you have to basically guess whether people subscribe to your definition of "right" before you can understand something.