I thought TDD meant doing tests before implementing code rather simply testing code.
So I always assumed someone testing his code wasn't necessarily TDDing, and that someone not TDDing wasn't necessarily not testing, just that she tests after implementation.
Is my understanding of TDD wrong ?
You are correct.
I incorrectly interpreted "don't do TDD" as "don't do tests".
I always thought it meant DRIVING the design as well.
The term TDD gets conflated with unit testing, and testing in general that it gets quite confusing have a discussion without going into hyperbole.
Code with no test coverage will have more defects and will be more prone to regressions.
For many projects TDD is the best we've got until something comes along that replaces it.