Plot Line Crossover

A plot point which seems to belong to Plot A belongs to Plot B also/instead. The plotlines aren't actually related, so we're not Working the Same Case, but a point or character introduced as related to one line ends up being important to the other.

Compare to Two Lines, No Waiting, Working the Same Case, Strange Minds Think Alike. If Plot B is sufficiently minor as to make you wonder "What's it doing here?", then the character is Chekhov's Gunman.

Not related to ordinary Crossovers, Intercontinuity Crossovers, or Mega Crossovers.

Examples of Plot Line Crossover include:

Literature

Peter Lovesey's The House Sitter: Peter Diamond investigates the murder of a profiler who was tracking a serial killer called The Mariner. Maybe The Mariner killed her, but maybe it was her jealous boyfriend. Well, she was killed in a somewhat random act, not by The Mariner. And by the way, The Mariner is the boyfriend.
Robert Van Gulik's The Lacquer Screen had several separate storylines. The killer in the A plot was a character in the B plot; the character in the B plot was introduced in the C plot, and the killer in the C plot was from the D plot.

Live Action TV

Friends episode "The One With the Videotape": the B plot involves Monica and Chandler being given fake names by a couple they met. To illustrate that people do this, Joey introduces himself as "Ken Adams." The A plot involves a seductive story Rachel tells Ross, unaware Joey already told him the story. When questioned, Rachel sputters that she heard the story from a friend, who heard it from a guy named Ken Adams.
The later seasons of Seinfeld do this often, many times a mixture of this and Strange Minds Think Alike?
All versions of CSI beat this trope to death in multiple episodes, such as finding a fingerprint of a suspect in the Plot B crime at the scene of the Plot A events.
Babylon 5 did this a bunch. For example, "The Quality of Mercy," with Laura's clinic and the murderer Mueller.
How I Met Your Mother episode "The Naked Man" has plot A with Barney and Ted trying out a new tactic called the The Naked Man (no points for guessing what they do) and plot B is Lily writing a list of 50 reasons to have sex, which she completes after trying The Naked Man tactic (2 out of 3 times people!)
An episode of Castle had two teams of detectives competing (and betting) on who was going to solve their respective cases first, they were forced to a draw when the two cases were related.

Other

Used on regular basis in Super Robot Wars.
The play and the movie versions of A Funny Thing Happened on the Way to the Forum have a lot of these.
Neil Simon's Rumors had this with Carol Newman
The Simpsons episode that showed the same day from three perspectives walks the line between this and Working the Same Case. There are probably many other Simpsons examples, they like to trip up the Two Lines, No Waiting formula from time to time.
- From the episode "Jazzy and the Pussycats," when the animals Lisa's raising injure Bart's arm:

Lisa: I feel so terrible. I just wanted to save those animals while Bart became a drummer, but I never thought the two stories would intersect!

Lampshaded in an episode of Futurama: Amy loses a present from Kiff when it falls into a whale tank and the whale swallows it. When she mentions it to her co-workers, Leela remarks "As unlikely as it may sound, I have an in with that whale"; earlier in the episode she bought a "Swim with the Whales" pass at that same aquarium.