You may not have known there was a difference between button-up and a button-down shirts — and while it's largely semantic, this video describes both types well, so you know what you're looking at the next time you shop.
What you call these buttoned shirts has nothing to do with whether you start buttoning the shirt from the top or bottom, but everything to do with whether they have buttons on the collar. If you can button down the flaps of your collar to the shirt itself, then you have a button-down. Otherwise, you have a button-up, which has no buttons on the collar.
Similarly, a button-down can also be called a button-up shirt, but not all button-ups can be a button-down. The video explains, but if you ever see both names and wonder what the difference is, now you know.
Here's the difference between a button-up and a button-down shirt [Business Insider]