Short answers, pulled from the story.
A media franchise is a collection of related works derived from a single original creative property, such as a film, novel, television program, or video game. Bob Iger of the Walt Disney Company defined a franchise as something that creates value across multiple businesses and territories over a long period of time.
A transmedia franchise specifically refers to a franchise that spreads content across multiple media platforms, with each medium expanding the story and audience. The simpler term media franchise is often used interchangeably, though scholars treat transmedia as a more specific concept.
Media mix, or mediamikkusu, is the Japanese term for a transmedia franchise strategy that disperses a property across broadcast media, gaming, cell phones, toys, amusement parks, and other formats. The term gained circulation in the mid- to late-1980s, though the strategy traces back to the 1960s with the spread of anime.
Pokémon began as a video game on Nintendo's Game Boy in the late 1990s and expanded into television, film, news coverage, trading cards, and merchandise. Its entry into the American market helped establish wider recognition of concepts like transmedia storytelling and media synergy.
Canon content refers to releases that belong to the main story and timeline of a franchise. Non-canon material uses franchise characters or settings but does not count as part of the official story; the Battlestar Galactica comics are a noted example, with only some issues considered canon.
Playboy Enterprises is a comprehensive example. Starting from the Playboy magazine, the company expanded within a few years into a modeling agency, television shows including Playboy's Penthouse in 1959, and eventually into clubs, restaurants, movie theaters, a radio show, clothing, housewares, and numerous other product lines.