If it helps you understand, originally cable tv was a way to pay for tv (as opposed to free OTA) that then had no ads, almost like how HBO operates today. Of course, that could only last for so long.
Cable TV was originally a way for communities outside of broadcast OTA TV reception areas to receive TV signals with little signal-degradation. People paid only for the ability to receive channels - not for the channels themselves. Premium TV came later.
Yes. Here's a little historical tidbit: if you have an older TV, you'll need to put your TV in CATV mode in order to watch cable. CATV stands for "community antenna television", referring to the practice of having one antenna to receive OTA TV and then using cable to distribute it throughout the community.