Good question. It can be quite confusing. Here's my attempt at making it "not" confusing. lol
Network: The buyers in the TV world. People come to a network with an idea. The network purchases the idea, then guides it along to what will eventually air on the network. Networks develop relationships with studios and production companies to bring them in on deals where they see fit. The network oversees the entire production each of their shows but they bring in studios and prod. co's to work in specific areas. Networks: ABC, CBS, FOX, NBC, and so on; Cable (Networks): ABC Family, BET, BRAVO, FX, VH1, and so forth.
Studio: The sellers in the TV world. Studios are always looking for the next great writers and/or stories to be told. They help the writer develop the pilot script for the particular Network(s)' brand in which it fits. The studio then sets up the pitch meeting with the network. If the network buys the show, they must then work with the studio to produce the show. (Produce as in "make" the show, not as in the title "producer.") A studio can often be a middle man. Not all writers go through a studio to get to a network. Writers can pitch directly to networks. The network will then decide if they want to bring in a studio as a part of the development process. Studios can work with as many different networks as they choose. If a studio and network have the same parent company, of course they'd like to stick with blood, but ultimately, the studio is working for itself and looking for the best deals. Studios: 20th Television, Happy Madison, Kaplan Entertainment, Mark Gordon Co., Sony Pictures Television, Warner Bros. TV, the list goes on.
Production Company (Prod. Co.): The production company handles the actual production of the show. They handle budgeting, scheduling, casting, hiring of the crew, postproduction, distribution, and even fundraising/financing the production. Production companies can be owned by larger parent companies (the network) or totally independent. Production Companies can also work together on a show as a co-production, meaning they are co-doing all of the business aforementioned. Production Companies: Bad Hat Harry, Bad Robot, Endemol, Harpo Productions, Lions Gate Entertainment, Marvel Television, to name a few.
So, it sounds like a network, studio, and production company do the same thing. Well, you're right. Lol. Not really, but sure. They all work together to get programming on your television. They each have a niche (Network: branding the programming and buying within the brand; Studio: finding the right stories and writers for a network's brand; Production: getting all of the people together to physically make the programming ). Voila! Hope you're now "not" confused.