Let's say smoke is escaping through a close door. It would be escaping through the space between the door and the floor or the wall, or perhaps between door and the jamb. Is there a term for that? Or is there an expression for that (perhaps: smoke seeping through the door? but that would suggest that it goes through door, rather than the space between the door and the floor or jamb).
Door gap is the general name for all of the gaps around the door.
The best method for measuring door gap dimensions is to use a tool of the appropriate thickness that can be inserted between the door frame and door, the door and the floor, and between opposing vertical edges (aka, meeting stiles) of paired doors. (Doorgapgauge.com, emphasis added)
FLOOR CLEARANCE: The distance between the bottom of the door and the top of the material directly below the door. This varies with applications, such as concrete, any floor covering and/or a threshold.
This gap is also called bottom clearance, and the top gap is called head clearance, while the side gaps are called stile clearances at taylordoors.com.
To class them all together, you could say "The smoke is seeping through the door gaps."