Then it's TDD that I have a problem with.
My main challenge is that I don't know what to call the tests I write, or the process that I use. Calling them "tests" can be confused with manual testing. I usually call them "automated tests" but it's a mouthful and not a term I hear from other people.
You call the tests you write tests. I'm not even sure how this is a question. Manual tests and automated tests are terms used in industry, but mostly to distinguish manual versus automated end-to-end or integration tests. And then the only time you'd use the terms is when you have both and feel a need to distinguish them. Otherwise, just call them tests.
What? The whole point of TDD is that you design the thing by writing the tests. That's why it's called Test Driven.