They both generally mean the same thing. The big difference is that "TV Show" might refer to one or multiple episodes of a specific show on television, while "TV series" usually refers to all episodes of a specific show on television.

GENERALLY, when most people say TV series, they are referring to fictional show that progressives episode to episode, or at least has a larger, overarching theme that connects all of the episodes over the course of the shows existence, even if they aren't connected episode to episode. Being extremely technical, all shows are series, but people don't usually refer to talk shows, news, etc as series.

Thank you for help!