Distinctions are a bit like Aspects, yes. At least in the MHRP version (which is the one I know), Distinctions serve both as components of the dice pool (either at d8, or at d4 and earn a Plot Point) and also as targets of action. Eg if the scene includes a Buildings On Fire Scene Distinction, then to extinguish the fire the heroes need to eliminate that Distinction. In my fantasy games we've also used Scene Distinctions for more "metaphysical" elements like Pursued by Orcs (eliminate the Scene Distinction to evade the pursuers) or Uncertain of What to Do Next (when the ranger in our LotR game eliminated this he was able to set the group's goal for the next scene.
SFX are similar to stunts, yes (I say that without being any sort of Fate expert). Mostly they allow for dice pool manipulation of various sorts, or stepping up certain effects inflicted or avoiding/reducing certain incoming effects.
Milestones are different from anything I know of in Fate: they are descriptions of events that happen (eg
give a team member advice or
inflict trauma on a foe or
lead the team into battle, etc) and when the character does that thing XP are earned. In practice - at least in my experience - what milestones do is create a player-side to the action, as the players look for ways to have their PCs achieve their milestones and earn XP - which runs alongside the GM side to the action, of the settings and foes etc. I think it emulates comics and a lot of other adventure fiction well, as the character drama and character arcs unfold somewhat independently of whatever the particular action is that is happening at a given moment.
To perform an action you build a pool - in MHRP that's one affiliation (solo, buddy or team), one Distinction, one power from each power set (if applicable), one specialty (if applicable - in D&D terms this is roughly the same as skills), any assets or resources that are applicable (roughly, these are gear or other situational benefits that have been built up through prior actions), any debuffs on the opponent (eg injuries or complications), and any bonus dice gained by spending plot points (eg to include a second specialty or second Distinction).
The player gets to add two dice to generate the roll total (extra dice can be added by spending points) and use another die as the effect. All checks are opposed, and so (unless you have an SFX that says otherwise) you only achieve your effect if you tie against or beat the opposition with your roll total.
Your effect depends on die size, not die roll - so having 10s and 12s in the pool is a big deal even if they roll poorly, as they give good effect dice. All effects are rated in dice, which are then applied as debuffs (stress, complications) or to step down other ratings (eg a d8 or greater effect will eliminate the typical Scene Distinction) or to create assets (which could be gear or a situational advantage or any other change in the fiction that benefits a character). I think this idea of rating everything in dice is mechanically different from Fate.
When Gandalf fights Orcs with Galmdring the pool might be d6 BUDDY (let's say he's fighting alongside Aragorn), d8 WIELDER OF THE FLAME OF ANOR (because when fighting servants of Sauron Gandalf's own power as a servant of Iluvatar comes to the fore), d8 for WEAPON plus d6 for the Foe-hammer SFX, and d8 for COMBAT EXPERT. He could also put in d8 for ENHANCED STRENGTH because that helps in a sword-fight against orcs.
So that would be a (pretty good) pool of 2d6+4d8. He could also use Servant of the Secret Fire to make the d8 from Enhanced Strength a d10 instead, with the risk that a failure will add a d8 to the Doom Pool.
If Gandalf succeeds (all checks are opposed - in this case it would be vs the orcs but if there's no active opposition then it's vs the Doom Pool) then one of his dice becomes an effect based on size and, because of Foe-hammer, would be stepped up by one (eg d8 to d10).
I think the other versions of the system use smaller pools than I'm used to from this MHRP version, but of participants in this thread
@Aldarc is probably better placed to address that.
This starts at 2 to 4 dice of size d6 to d10, depending on the scope and stakes of the drama as decided by the GM. In our LotR game it was 2d8. The Doom Pool grows over time, mostly by paying players Plot Points when they roll 1s, but in various other ways also (eg when a NPC uses a character Distinction at d4 rather than d8, which would earn a player a plot point, the GM instead gets to grow the Doom Pool).
These dice do three things: (1) they are the opposition for player rolls when there is no active opposition in the fiction; (2) they are a source of "points" for the GM to spend to activate SFX or add to the GM's pools, analogous to plot points for the players; (3) it serves a pacing function, especially because the GM can spend 2d12 from the Doom Pool (if they're there to be spent) to peremptorily end a scene.
Learning how to manage the Doom Pool is, at least in my view, the hardest thing and most important skill in refereeing this system. But I don't know if Cortex Prime or MotU will use this mechanic. Personally it's one I really like, although it has some quirks because of the multiple roles it plays. As I already said I don't have much Fate-fu, but I think a difference from Fate is that the GM doesn't have a limitless pool of aspects or opposition - the Doom Pool constrains this in interesting ways.
