You are conflating movie ratings and television ratings being displayed, with the content of the programs that are being aired.
Broadcast television is subject to the most regulation, as the airwaves are considered to be public property and must be licensed from the government, which attaches many strings, including regulation of content. Even then, the most strict regulation applies between the hours of 6 am and 10 pm local time, when it is assumed that the highest number of children may be watching. The broadcast television industry self-imposes restraints on content between 10 pm and 6 am, mostly out of fear of fines and other punishment by the FCC.
General cable channels on the other hand enjoy much more freedom on what they transmit, since cable is not limited by 'scarce' broadcast frequencies and, according to one judicial opinion, restriction "'implicates First Amendment interests', since a cable operator communicates ideas through selection of original programming and through exercise of editorial discretion in determining which stations to include in its offering". Multiple attempts by both Congress and the FCC to regulate content on cable in a manner similar to broadcast television have been rejected by courts on First Amendment grounds.
One of the only restrictions that has survived court challenges is that cable operators must provide, at no charge, the ability to block or scramble any channel to which a customer has not subscribed. (Even this was reduced from a restriction passed into law that required operators to prevent signal bleed of pornographic material by either always scrambling any channel containing it, or not airing the material at all, between the hours of 6 am and 10 pm.)
All of that said, the cable television industry has for many years also self-regulated content, simply out of fear of angering viewers and driving away advertisers. In recent years, though, some channels - primary examples include FX and Comedy Central - have loosened these "Standards and Practices" restrictions. Channels now regularly air R-rated movies without cuts, and twenty-five years ago, a show like South Park would have been unthinkable outside of a channel like HBO.
As you note, premium channels show more mature content than their regular cable counterparts. This is partly due to the above-discussed non-regulation of cable television, but also because they do not have advertisers to which they must answer. Viewers angered can simply stop paying for the channel, and while a loss of subscribers is not a good thing for a channel that is mostly or entirely funded by subscription revenue, quality mature programming has a significant market size.
Separate from all of the above, television ratings are a "voluntary" system (set up with the cooperation of the broadcast industry, Congress and the FCC, but not officially regulated by government) with no legal force behind them. V-Chips have been required to be included in all TVs manufactured for sale in the US since 1999 by a law passed under Bill Clinton, but the V-Chip uses the ratings voluntarily placed on programming by the industry. Generally speaking, regular cable channels rate all programs (except sports, news and commercials, which are not rated on any channel, cable or otherwise), and premium channels use a mix of MPAA movie ratings and television ratings, depending on the content being shown and (in the case of previously-rated movies) if it has been edited since the original rating was assigned.