Delta Air Lines has uncorked a rebranding of all of its fare types — upending the Basic Economy/Main Cabin/Comfort Plus/etc. order that has dominated the big U.S. airlines for the last decade or so.

I spent $205 on a basic economy flight with United Airlines from New York City to Denver. A few days later, I took a $175 basic economy flight with Delta from Salt Lake City to NYC. Both flights were ...