The Realm of Shadows may be the same World of Shadows as the one that becomes visible when a [Elixir of Shadows] is consumed. It may also have something to do with shadow magic and shades. Death knights, necromancers, and undead as a whole share a strong connection with the Realm of Shadows from many hints that can be seen in-game. In the death knight starting zone, death knights are given the task to enter the Realm of Shadows in order to gain their Deathcharger. Later on, death knights are eventually able to learn the ability [Raise Ally] which pulls their ally's spirit back from the Realm of the Dead and forces it back into their body. Upon doing so, a buff is applied to the player stating that: "A touch of the spirit realm still lingers..." This shows that death knights and necromancers both have a connection to the Realm of the Shadows/Dead to perform necromancy which furthers the idea that they actually are drawing their magical power from it.
During the Burning Legion's third invasion, the Knights of the Ebon Blade traveled to the Shadowlands to acquire the Aggregates of Anguish, five tormented essences of powerful souls - Admiral Proudmoore, Soulbinder Nyami, Grand Empress Shek'zeer, Grand Apothecary Putress and Archmage Arugal. Salanaar required these to conjure the Steeds of the Damned for the order's new Horsemen.
The spell called "spiritual projection" or "astral projection" brings the caster to the Twisting Nether instead of the Shadowlands; and the Twisting Nether is also referred as "realm of ghosts". However, both planes don't appear to be related, as Outland is floating on the Twisting Nether, but the Shadowlands can be reached in Outland in The Burning Crusade.
Sometimes, the spirits roam the Shadowlands without resting. It can be because their resting place wasn't complete, because of a battle in their resting place or because of the corruption of their resting place. To bring eternal peace to the souls, it is needed to destroy the source of corruption or by making a ceremony with items such as [Tuskarr Ritual Object]. A spirit in the Shadowlands can, with enough power over other souls, tear a hole into the living world once they are strong enough. This is how Jin'do returned to Azeroth.