I agree with Rob Stevenson-Leggett that there is a distinction, and I think between being a programmer and an agile programmer is a mindset change.
I am an agile programmer working for a company that is still trying to move from no process or standards to having something better in place, but they don't know where they are going, so there are some struggles at times as I see development differently.
For example, with agile, you should release often, so that the users can see what you are doing, and help to correct if it isn't what they want. That is different than waiting until all the specs are implemented and tested. I would prefer to get something done, then as I get some features finished re-release.
But this also requires good bug tracking, so the users, or someone that interacts with users, can submit bugs and see what the state of them are, good version control, ideally with at least nightly builds and peer-reviewed unit testing.
Unit tests should be reviewed, at least initially, because bad unit tests are worse than no tests. If I know there are no tests I approach the software differently, but if the unit tests are very poor then I may trust that the code was tested and run into more problems later.
For example, I recently had a chat with a couple end-users where I asked "What kind of questions will you be asked to justify the cost of this software". I am looking for what should be measured. I don't care for them to get into details about storing IP addresses or how to track users, they just need to tell me what type of questions need to be answered, as they create reports, or their superiors are curious, as I can't give them the info if I don't know what to collect.