Twenty Minutes Into the Present

It's the sequel. The previous film was made in 1980, this one came out in 1981. The opening sequence renders all the previous heroes of the first film killed off by the monster who turned out to be Not Quite Dead. There are credits, and after the credits a title pops up informing us that it's "Five Years Later..." A new bunch of characters move into the now abandoned cabin but encounter the same thing as the previous bunch of characters.

Being set in the near future, the movie shouldn't feature contemporary album posters and advertisements, but it does because only the characters have aged five years; the world stays the same age.

Contrast Comic Book Time, where characters stay the same age while the world gets older; Present Day Past, where a work set in the past (not necessarily part of a series) contains contemporary references.

Film

 * The Friday the 13 th series: Each sequel jumps a minimum of five years, placing part 8 sometime in the late 1990s, but the 1989 Batman film is advertised heavily in Times Square.
 * The 1930s The Mummy movies: If you took the year the first movie was stated to take place in, then added the time skips in each subsequent movie, the last movie would have taken place in the 1980s.
 * Halloween
 * From 2 to 4: 10 years.
 * 4 to 5: one year.
 * 5 to The Curse: Six years.
 * A Nightmare on Elm Street
 * Rise of the Planet of the Apes never makes clear what year it's supposed to be in, although the script sets the first scene in 2011. Then eight years pass in which Caesar becomes an adult and leads the rebellion of the apes, but none of the human characters or the world around them gets any older.

Live-Action TV

 * 24: Each successive season jumps about 2 years, but it's still the same year the show airs in.
 * Desperate Housewives does this with its multiple time-skips.
 * Alias skipped ahead a couple/three years once.
 * Starman, the TV series, followed Starman, the film, two years later. Both are set in the 1980s, but in-story there's a fifteen-year gap between them.