The Terms Extradimensional Space and Nondimensional Space Are Interchangeable

This becomes clear when looking at how the terms are used in context. The most useful example is the portable hole (DMG 264) (20,000 gp; 0 lbs.), which says that it

is a circle of cloth spun from the webs of a phase spider interwoven with strands of ether and beams of starlight. When opened fully, a portable hole is 6 feet in diameter, but it can be folded up to be as small as a pocket handkerchief. When spread upon any surface, it causes an extradimensional space 10 feet deep to come into being. This hole can be picked up from inside or out by simply taking hold of the edges of the cloth and folding it up. Either way, the entrance disappears, but anything inside the hole remains.

The only air in the hole is that which enters when the hole is opened. It contains enough air to supply one Medium creature or two Small creatures for 10 minutes. (See Suffocation, page 304.) The cloth does not accumulate weight even if its hole is filled (with gold, for example). Each portable hole opens on its own particular nondimensional space. If a bag of holding (see page 248) is placed within a portable hole, a rift to the Astral Plane is torn in that place. Both the bag and the cloth are sucked into the void and forever lost. If a portable hole is placed within a bag of holding, it opens a gate to the Astral Plane. The hole, the bag, and any creatures within a 10-foot radius are drawn there, the portable hole and bag of holding being destroyed in the process. (DMG 264)

Emphasis mine. Thus, even within the portable hole's description, the terms extradimensional space and nondimensional space are used interchangeably. That's because such spaces are--no matter which term is used--technically demiplanes:

This catch-all category covers all extradimensional spaces that function like planes but have measurable size and limited access. Other kinds of planes are theoretically infinite in size, but a demiplane might be only a few hundred feet across. Access to demiplanes may be limited to particular locations (such as a fixed gateway) or particular situations (such as a time of year or a weather condition). Some demiplanes are created by powerful magic, some naturally evolve, and some appear according to the will of the deities.

In the D&D cosmology, also known as the Great Wheel, the planes are connected in a specific fashion, as depicted in the diagram on page 153. (The diagram does not show demiplanes, because the location and even the existence of these extradimensional spaces is constantly changing.) (DMG 147)

Therefore the extradimensional spaces of the bag of devouring (DMG 274) (n/a gp; 0 lbs.), the mirror of life-trapping (DMG 262) (2000,000 gp; 50 lbs.), the 2nd-level Sor/Wiz spell rope trick [trans] (PH 273), and the 7th-level Sor/Wiz spell Mordenkainen's magnificent mansion [conj] (PH 256) are the same kinds of spaces as the nondimensional spaces of the bag of holding (DMG 248) (2,500+ gp; 15+ lbs.), the pocket paradise created by the rod of security (DMG 236) (61,000 gp; 5 lbs.), and the quiver of Ehlonna (DMG 265) (1,800 gp; 2 lbs.).

Speculation
The Player's Handbook uses exclusively the term extradimensional space, while the Dungeon Master's Guide mixes the terms extradimensional space and nondimensional space freely. I think it was one of those things the authors never expected anyone to care about, hence not worth fixing... not expecting that over a decade after its release such term mixing would bother careful readers of their game.

Detailed information on the 5e version of the Shadowfell is still pending (hopefully in the Dungeon Master's Guide!) but here are some typical inhabitants from 4e:

• Shadar-Kai, near-humans with tattoos and scars that rejoice in battle and have shadowy abilities.
• Shadow creatures (none are in the Basic Rules bestiary, and the type may not exist at all in 5e).
• Ghosts of the dead on their way to their final destination.
• Corporeal undead, typically the result of ghosts who refused to pass on.
• Any horror-themed creature, as the Shadowfell is basically Spooky Halloween World.

Given the limited creatures available in the Basic Rules, I'd provide a lot of undead and reskin some other creatures: turn wolves into "balehounds" and ogres into "flesh terrors" and so on.

You can generally assume that each normal race has a Shadowfell subrace or equivalent with gray skin, shadow-themed abilities, and more piercings.