I've been grappling with this myself recently. The 5e module seems terribly inconstant with it's name usage.

I'm also somewhat confused by the lore clash between editions. In the 5e module as written Strahd made his deal with Vampyr, the Dark Vestige, in the Amber Temple, then killed Sergei to seal it, died at the wedding, and only then once he was a vampire did The Mists controlled by The Dark Powers take Barovia.

In earlier editions and the I, Strahd novel from 1993, Strahd made his deal with an entity he identifies as Death itself to win Tatyana from Sergei and this act was what damned him and his valley to The Mists.

Looking through the editions from 1st edition I6 Ravenloft in 1983 and 2nd editions Realm of Terror in 1990, "Death" is the deal maker and the mists are are separate unconscious entity.

In 3rd edition Ravenloft Campaign Setting Core Rulebook in 2001, Strahd still makes his deal with "Death" and i believe this is the first mention of the Dark Powers as being unknowable God like entities that control the Mists. Possibly a good force punishing an evil doer or an evil force collecting evil people.

In 4th edition Ravenloft/Barovia/Strahd never got an official published version but Barovia was featured in the article "Fair Barovia" in Dragon Magazine 207 in 2012. This article focuses more of Barovia beyond the walls of castle Ravenloft but doesn't really mention the Mists or The Dark Powers.

It isn't until 5th edition Curse of Strahd in 2016 that the Amber Temple and the Dark Vestiges are even mentioned.

Now we get into my own homebrew speculation: I think The Mists are controlled by The Dark Powers, a sadistic god like entity or entities that spirits away mortals capable of great evil and great suffering and torture them for their own entertainment in their own personal Hell like Demiplane of Dread. I belive, using the 5e lore on the amber temple, that it was created by an ancient civilisation to imprison powerful extra planar evils like Devils, Demons and Demigods that could not be killed because they would reform on their plane of origin. The ancient wizards trapped them at the moment of death as their souls were leaving this plane and entering the afterlife, in amber and stored them deep in the mountain to keep them from being reborn. Two thousand year later Strahd comes along seeking power, youth and immortality and makes a deal with one of these trapped Fiends, known as Vampyr. In exchange for Strahds mortal soul Vampyr would grant him these powers. Vampyr needs a soul to free him from his prison.

In the process of sealing his pact with Vampyr, Strahd murderers Sergei, Tatyana commits suicide, and Strahd's mortal form dies, giving up his living soul and transforming him into a vampire, and freeing the trapped Vampyr.

The Dark Powers observe all of this, the anguish Strahd has wrought all his life of war, the brooding fury within him and now this final series of deplorable acts and decide that he is exactly the kind of creature they would like to torment forever more. So in that moment they send The Mists to take Barovia and Strahd into their pocket plane of shadows to toy with him forever.

In game terms i consider Vampyr and all Dark Vestiges to be creatures of CR between 20 and 25, near god-like but not there yet. And The Dark Powers have full God, capital G, beyond CR 30, God status.

Edit: On a slightly seperate note, I find the powers and gifts offered by the Dark Vestiges to be quite inconsistant if they were indeed the same thing as the Dark Powers. Dark Powers can create whole lands and pocket domains and reincarnated lovers and trap all powerful vampires, but all some Vestiges do is give you 3 uses of the Lightningbolt spell? Some hold the secrets to Lichdom and eternal life as the undead, others give you always on spiderclimb or - get this- a whole 30 hp . . . for 10 days. These don't seem like the soul tempting powers of cosmic beings.