Demiplanes are extradimensional spaces. Which extradimensional spaces are also demiplanes is ultimately up to the DM, but they should be large enough to enter for the PCs
One thing we can say for sure is that demiplanes are extradimensional spaces. The converse is probably not true: extradimensional spaces are not neccesarily demiplanes, but we lack clear rules to say which are, and which are not.
The entry for Demiplanes on page 68 in the Dungeon Master's Guide says:
Demiplanes are extradimensional spaces that come into being by a variety of means and boast their own physical laws. Some are created by spells. Others exist naturally, as folds of reality pinched off from the rest of the multiverse. Theoretically, a plane shift spell can carry travelers to a demiplane, but the proper frequency required for the tuning fork would be extremely hard to acquire. The gate spell is more reliable, assuming the caster knows of the demiplane.
A demiplane can be as small as a single chamber or large enough to contain an entire realm. For example, a Mordenkainen 's magnificent mansion spell creates a demiplane consisting of a foyer with multiple adjoining rooms, while the land of Barovia (in the Ravenloft setting) exists entirely within a demiplane under the sway of its vampire lord, Strahd von Zarovich.
The the lower end of the size dimension range given for a Demiplane is as small as a single chamber, and that would be larger than the extradimensional space created by a magic item like a bag of holding or a quiver of ehlonna. A rope trick hidey-hole however would qualify.
Of course "as small as a single chamber" is elusively vague. A single chamber for a tiny pixie sorcerer could indeed be quite small, maybe even a cubic foot might suffice, and the text does not constrain for whom the chamber may serve. It also leads to problems as why a 10x10 foot room would be a demiplane, but a, say 5 x 5 foot room would not be.
The PHB describes Demiplanes like this on page 302:
Demiplanes are small extradimensional spaces with their own unique rules. They are pieces of reality that don’t seem to fit anywhere else. Demiplanes come
into being by a variety of means. Some are created by spells, such as demiplane, or generated at the desire of a powerful deity or other force. They may exist naturally, as a fold of existing reality that has been pinched off from the rest of the multiverse, or as a baby universe growing in power. A given demiplane can be entered through a single point where it touches another plane.
This reiterates that extradimensional space is the supertype, and demiplane is a specific subtype that typcially is "small". Ravenloft has the size of an entire realm (as mentioned in the DMG), so small here would mean in relation to an entire world, planet, or universe.
We also know this description does not fit all demiplanes: Ravenloft can be entered through the mists from anywhere, not at a single point.
Demiplanes can have special rules and physics
What may be more important instead, is that a demiplane can have its own, special rules: this is consistent between the PHB ("their own unique rules") and the DMG ("their own physical laws"). For example, the MMM spell claims "The atmosphere is clean, fresh, and warm.", the Maze spell has rules that allow a creature to leave the plane, the Hedged Prison option of Imprisonment creates a "tiny demiplane that is warded against teleportation and planar travel."
If there is no hard limit on size, because rooms for tiny people could be very small, and if you count the dimensions and rules about air in a bag of holding as special rules, that would make the bag's space a demiplane, and the quiver's space (lacking such descriptions), not.
A non-demiplane extradimensional space may just inherit the rules and physical laws of it's parent dimension or plane. Of course, the definition of such rules does not preclude that the demiplane also can have matching rules -- for example, the demiplanes created by the eponymous spell mention nothing special about the rules of physics that govern them, and normally, a spell needs to mention things to be able to do them. The only limitation it has is its size and the look of its walls and floor.
Why does this even matter?
The distinction however has some surprisingly practical implications. As the text in the DMG outlines, you can plane shift or gate into any demiplane, while no such thing is said about extradminsional spaces in general.
If this would work on any extradimensional space, then you could for example open a gate to a bag of holding or portable hole you know about, and plunder its contents. In high level play, this is a very practical consideration.
Gating or plane-shifitng into small spaces also would cause other problems, for example if the demiplane was tiny, too small to actually contain a small or medium-size spellcaster. Would they be squashed to death?
For practical reasons, I think it is better to consider not every extradimensional space as a demiplane, only those large enough. Mordenkainen's magnificient mansion, that is cited in the example, is. The maze created by a Maze spell explicitly is. A bag of holding might be (it can house a creature), the space created by a quiver of elhonna, would not be.
In the end however, there seems to be not enough consistency in the use of the words "extradimensional space" or "demiplane", even within the core rule books, to really differentiate them clearly, and no clear or hard rules to do so. For example, the MMM spell itself does not call what it creates a demiplane, it just calls it an extradimensional space. So, it will probably be up to the DM how he adjudicates what extradimensional space is, and what is not, a demiplane.
