Indeed, they are two separate concepts.
I write lots of automated tests, but almost always after the development is finished. The only exception is when reproducing a bug, where I first write the test that reproduces it, then I fix the code.
TDD is about developing tests first then writing the code to make the tests pass. I know several people who gave it an honest try but gave up a few months later. They do advocate everyone should try the approach, though, simply because it will make you write production code that's easier to test later on.
... hmm, just looked it up. According to some sites on the web, TDD was created by Kent Beck as apart of Extreme Programming in the 90's and automated testing is a big part of TDD. Having lived through that era, thinking back, would say that TDD did help to popularize automated testing. It made us realize that focusing a ton on writing tests had a lot of benefits (and yeah, most of us didn't do the test first development part).
But this is kind of splitting hairs on what TDD is, not too important.