Ok, let's try to explain this through layers.
First, you've got the lands of the body, matter, living or skin. That is Earth, three dimensions, four cardinal points, that stuff. Easy to understand since it is where most characters live and is based on where we live.
Then, because of some cosmic problem never fully explained, the spirit world got divided a long, long, long time ago. There is now a barrier between them. This is the first of many barriers, some with the same name, so lets not get confused, and it is called Gauntlet. The Gauntlet separates physical Earth and the nearest part of the spirit world, called Penumbra which is a spirit reflection of the physical world. It is technically ‘overlapping’ the Earth.
You can ‘sidestep’ this part of the Umbra and go directly to other parts of the spirit world called ‘Near Umbra’ that are also separated of the physical world by a barrier called Gauntlet (whether it is the same as the Penumbra one, I will leave to discuss). The ‘Near Umbra’ is composed of this new (or not so new) Gauntlet, the Spirit Wilds, the Astral Umbra and the Shadow World. Although there is no ‘real’ direction in the Umbra, we usually say that the Spirit Wilds are in the ‘middle’ (that’s why we call it ‘ Middle Umbra’), the Astral Umbra is on ‘top’ (that is why sometimes is called the ‘High Umbra’) and the Shadow Lands on the bottom (which, not surprisingly, is sometimes called ‘Lower Umbra’, but it is also called ‘Shadow Umbra’). This is reinforced (or maybe because we think like this, you never know in the Umbra) by a place in Umbra where there is a tree that if you go ‘down’ its roots, you reach the Shadow Land, and if you ‘climb it’ you reach the Astral Umbra (I don’t remember the name of this place, but I believe it is in the book of worlds).
The Astral Umbra is technically the place most visited by Mages and is quite well mapped. You can read more on the infinite tapestry and the book of worlds; the Middle Umbra is most visited by Werewolves, and it is composed by some realms (don’t remember the amount right now) which they visit, some more than others. You can read more of the Middle Umbra and its realms in Umbra The Velvet Shadow. Finally, the Lower Umbra is inhabited by Wraiths (among other things) and contains a lot of places that are out of scope of this answer, but if you want more info on them (such as the Labyrinth, the Tempest or Oblivion) you can read Wraith: The Oblivion.
In reality, each of these Umbra has a different Gauntlet with different names, but they behave exactly like each other. So the ‘Gauntlet’ is just a common name for a barrier that separates the physical world and the near umbra/penumbra.
Beyond these three Umbra, we encounter another barrier that separates the Near Umbra and the ‘things beyond’ (chan chan chaaan!). This new barrier is not as ‘smooth’ as the Gauntlet and you can say it has cracks in it. You can ‘fall’ into these ‘cracks’ and reach some special places called ‘zones’. Technically the Dreaming (from Changeling: The Dreaming) is one of these zones. The Virtual Adepts Digital Web (although it does not belong to the Virtual Adepts) is also another zone. Most of the zones are described in the book of worlds.
In this barrier, the Horizon that separates the Near Umbra from the outside beyond (again, chan chan chaaan!) is where most mages build their all-powerful (or not so powerful) Chantries. Concordia (the stronghold of hope for the nine traditions), for example, is located in this area.
What lies beyond is called Etherspace (I will let you guess by whom), and it is kinda like outer space. In some books it is also called True Horizon. We have some big rocks moving through here (some people call them planets, also the Sun) and each of them has it’s own specific Umbra, most of the time called a ‘Shard Realm’, These realms are representations of the absolute of one sphere (so, Mars is the representation of Forces, not a nice place to be). None of them are habitable. Fortunately, each of them casts a ‘shadow’ on the first Horizon barrier we talked about, creating the ‘Shadow Shard Realms’ that you may have heard of. For example, Doissetep is in the Shadow Shard Realm of Forces.
Beyond even that (in the book of worlds they put it more or less at the asteroid belt) is the Far Horizon, and it is the last barrier we will talk about. It is technically very difficult to cross due to asteroids travelling at high speed that can hit you (you do not want to calculate how much damage an asteroid does at high speed) and huge blasts of energy. In 2nd edition there where some safe passages that (mostly sons of ether) were used to reach Jupiter, Saturn, Neptune, Uranus and Pluto (and all their moons), but with the Avatar Storm and all the stuff that happened by 3rd edition, it was ‘impossible’ to pass.
On the other side of this last barrier, we have the Deep Umbra, where said planets (and their Umbra or Shard Realms) are. They also cast a Shadow in the first horizon that we discussed (basically, all the shards cast a shadow on the same horizon… convenient!). Paradox realms and some Chantries (like Cerberus, the biggest Chantry of the Euthanatoi) are here.
Beyond that, we do not have much info, but you can check the Void Engineers and their Null Threat (it could spoiler some stuff, so handle with care). Also, most of the stuff Nephandi summon to help them are from places like this (Deep-Deep Umbra), things that live between stars, outside the Tellurian and way beyond compression and sanity. Again, handle with care :)
