A Spiritual Successor is a type of sequel that is not part of the same world or story as its predecessor, but is nonetheless considered to be a successor because it's made by the same creators, shares common themes, styles, or elements; or, most likely, both. In other words, it's a sequel "in spirit".
A Spiritual Predecessor, on the other hand, is when a previous body of work has, somehow, paved the way for future, similar work, that is, again, not part of the same world, or universe, but shares a common connection in creators, themes, styles, or elements. In short, if it wasn't for the predecessor, other works might not have seen the light of day.
Examples are as follows
- Similar to the above mentioned, Bewitched itself also paved the way for other works to rethink its imaging of witches, thus, basically establishing the Cute Witch and Hot Witch tropes.
- Hanna-Barbera's The Banana Splits featured costumes and settings that were brought to life by Sid and Marty Krofft, and as such, impressed network executives, which opened doors for the Krofft brothers to venture into their own brand of Saturday Morning television.
- The Ed Sullivan Show helped garner Jim Henson national recognition, and a number of the skits, sketches, pantomimes, etc. that Henson and his team performed during their years appearing on the program were later established for the kind of humor and entertainment that became the focus of Henson's The Muppet Show.
- M*A*S*H set the bar for a many ensuing programs, whether for its medical accuracy and realism (ER, Grey's Anatomy), its balance of both comedy and drama (Desperate Housewives, Glee), utilizing multiple subplots per half-hour (Seinfeld), or its occasion forgoing of the laugh track (many of today's contemporary sitcoms omit laughter altogether, live or simulated).
- Both the original U.K., and the U.S. adapted versions of The Office established a new trend and tool for primetime television, with it's mockumentary-style story telling, paving way for other sitcoms, such as Parks and Recreation, Modern Family, The Middle, and others to do the same.
- Sesame Street is a big example of this, as it was the first of its kind in create a television series for young children that would both entertain, and educate them. The success of Sesame Street opened the door for a number of other such series, such as Barney & Friends, Teletubbies, Blues Clues, Dora the Explorer, and others (most of which, the creators have said they used Sesame Street as a model''.