The top screenshot is of the old version of the calculated field window.
The bottom screen is the new calculated field window.
There is no way to change it (other than using an older version of Tableau).
Hope this helps clarify!
That's unfortunate that I wasted so much time looking. Thanks for your quick response, Derrick.
Just to add to what Derrick said, the way the two screens function is also different.
in 8.2 you would click on a field name from the lower boxes, and T would pop them where your cursor was.
In 9.0 forward, you drag from your sheet instead of using lists from the edit screen. Or you start typing a field name and T gives you a pulldown list of items that fit what you're typing.
You can also modify the 9.0 edit screen. You can drag the shape/size of the screen. Also in the screenshot you gave, you'll see a little grey arrow to the left of "ATAN" in the functions listed in the 9.0 screen. Click that arrow and the function list goes away. (And the arrow reverses direction.) Click it again and the function list comes back.
Just a few of the changes. It took me a while to get used to it. I've been using it now since 9.0 came out, and the 8.2 screen now looks foreign to me and works awkwardly because I am used to the new format.