Baseball players wear caps. There are caps based upon the design of the baseball cap, e.g. the MAGA cap of Donald Trump fame. It is NOT a hat.
Consider the cowboy hat. It has a different look than a baseball cap. We don’t call them cowboy caps.
I think all these Ivy League geniuses that hang out in newsrooms should have learned the difference between a cap and and a hat. 🧢 🎩 .
American Football players wear helmets when they play, not hats.