It’s even more ambiguous when people say “200% faster”. What does 50% faster mean in a world where people can say 200% faster with impunity?

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.

The only reason to have “per cent” (%) as a concept is because decimal fractions weren’t invented yet when per cent was first used; until the past few centuries arithmetic was almost exclusively done in terms of integers or ratios (or various mixed units depending on the material being measured). Using 1/100 as a generic unit was a work-around to make numbers less than one easier to compare and recognize by turning them into 2-digit whole numbers instead of needing to do a careful computation to judge between say 5/13 vs. 3/8.

There’s not really any particular advantage to saying 0.005 of the amount (or 1 – 0.995 of the amount) vs. 200 times less. Personally I find it significantly less clear (though not really any more or less “impressive”), because doing mental decimal arithmetic takes some extra effort and leaves more room for confusion. That is, it is easier to reason about multiplying or dividing some quantity by 200 vs. multiplying or dividing by (1 – 0.995).

But the two numbers are reciprocals; this is grade-school rational arithmetic, not some kind of trick.