For some of the SWADE concepts this is a helpful series of short explainer videos:
https://www.youtube.com/playlist?list=PLkHjiWAUZQbrAHB1QXUul1BAQiQm-B4Jj
This is a longer video that goes into probably more detail than you need:
https://www.youtube.com/watch?v=Ol70OK2YQV0

But high level differences with D&D 5e:

No classes, more RP related character modifiers (Edges and Hindrances)

You roll different die types instead of a d20. Larger dice mean higher proficiency (e.g. d4 < d6).

All main characters (PCs and NPCs) also roll a second d6 called a Wild Die, and you take the higher of the Wild Die or your actual roll (don’t add them together). A 4 is a success most of the time, with raises for every 4 higher than that.

Instead of Crit Fail and Crit Success there’s Crit Fail and “Ace” or exploding dice.

  • Crit Fail = 1 on trait die and 1 on Wild Die
  • Ace = roll the highest number on the die (e.g. 6 on d6, 10 on d10). The die you ace with, you reroll and add to the previous total. Yes this can get ridiculous if you get lucky.

Initiative in combat and other trials is based on a playing card you redraw each round (rank, then suit).
So it changes round to round. Jokers are awesome and you want to draw them.

Combat is swingy and can be deadly. Instead of whittling away spell slots and HP you just have
“Wounds”. Taking Wounds is very bad and you want to avoid it. Luckily main characters also have
Bennies and can Soak.

Bennies are kind of like inspiration but way better. You get 3 to start and can get more from the GM in game.

They allow you to

  • Reroll anything except a crit fail (keep the best result)
  • Take a new initiative card (keep the one you want, edges only affect the first draw though)
  • Recover from shaken
  • Recover 5 power points
  • Soak wounds
  • Affect the story

The first three are pretty straightforward. The explainer videos explain this better but for soaking
wounds think of bennies as a shield and wounds as health in a sci-fi game. If you have bennies you’re health is usually safe, but if you lose your shield, you are going to take health damage and that doesn’t come back so easily. For the last it’s more of a case by case basis. Maybe you really did remember to pack that extra rope?