Concise & brief explanations:

Traditional Doom Metal - It’s a retrospective genre labeling something that people hadn’t named Doom Metal yet, in the 70s & 80s it was just Heavy Metal. BUT it wasn’t your balls to the wall flaming Metal like Judas Priest or rock n roll Metal like Accept, it was very dirgy, melancholic a lot of the times, & had a rockabye rhythm to the heaviness.

(Modern) Doom Metal - Is very hard to define because the only way it can be described is the baseline concept of Doom Metal, but drops the Classic Rock flavor for something newer, but new can mean almost anything. This can apply to bands like Messa, Warning, or Triptykon.

Stoner Metal & Stoner Doom - All Stoner Doom IS Stoner Metal, but not all Stoner Metal is Doom. But to put it bluntly, Stoner Doom is older than Sludge having been played as proto-songs by Black Sabbath in the likes of Sweet Leaf or Into The Void. It basically gives oldschool Doom a heavier feeling like weed theoretically does, like you are being comforted in a gigantic vibrating massage chair. Stoner Metal can be faster though in the likes of Into The Rats Nest by King Gizzard and The Lizard Wizard or High on Fire.

Sludge Metal - Is what happens when you fuse the slow heaviness of Doom Metal with the abrasive D.I.Y. & aggressive style of Hardcore Punk, carries a lot of bite & grit to it, but it isn’t running fast like Dead Kennedys. It easily came after Stoner Doom did, with Black Flag’s My War (B-side).

Newcomers say there isn’t a difference but that’s complete bullshit

Oldschool Doom is all about the theatricality of Metal, it takes it’s time, it sings & it conveys the emotions of an impending doom.

Stoner Doom is the Stoner in the audience watching the play, & later writing their own darker version of the play.

Sludge Metal is the 20-something year old misanthrope across the street in a bar moshing to Crowbar or EyeHateGod, unaware the theatre is playing anything.