"The fan breaks up the sound waves, which makes the sound seem less."
In this case it's unlikely, because ceiling fans spin at a low enough speed that they're very unlikely to cause sonic jamming, and any reflection of sound caused by the blades would distort the sound, not deaden it.
"The fan is about 15 feet away from the TV. They're on different outlets and the fan is so quiet that we often forget to turn it off before we go to bed. Turning on the floor fan that's on the same outlet as the TV produces no problem."
I assumed your ceiling fan is hard-wired, so that's why I suspected that it's sharing a circuit with the outlets, and if it's not properly grounded then it could be introducing RF interference or a significant change in power draw when you use it. A floor fan motor will draw quite a bit less current than a ceiling fan motor when it's running, and if it's properly grounded it won't cause the same sorts of problems. If you're feeling ambitious, run an extension cord from another room to the TV and see if that makes it stop.