A single stage will have a uniform resistance. A good one will break cleanly without any creep or over-travel. Very little trigger movement overall, unless it's a crappy trigger then it might have a lot of creep and over-travel like a mil-spec AR-15 trigger.
A two stage trigger will have some takeup with a long light trigger pull until you get to the break point. Once there it gets heavier and breaks cleanly a lot like a good single stage trigger.
Two stage triggers, IMO, are better for target guns or any precision shooting.
You get your sight picture and start pointing at what you're shooting, then pull until you feel the resistance of the second stage, then get everything finalized and follow through until you here the loud bang noise.
For a SHTF all-around gun, I'd go w/ a good tuned mil-spec single stage.
I prefer two stage triggers like the Savage Accu-trigger for hunting rifles. I prefer a good single stage adjustable trigger for target shoots. With the two stage, it will give you ability to know when the trigger will break and that can make your shots more accurate than a run of the mill single stage. Some don't like 2 stage triggers though and there's nothing wrong with that!! My single stage adjustable has no creep, no over travel and is set at 4oz's. When that dot centers in my peep/globe sights, I touch the trigger and it's there. The differences have already been posted and I've given you the reasons I use which one and where. The only thing that matters is what works best for you anyways.
for me one stage for fast trigger work like loco drills and the two stage is in all long range lowers, more sensitive.
I tune all my triggers myself. But this is me, there is no rule written about this.
IMO It is like life itself...
When dating is a "two stage" deal.
After married, hurry up! we got 5 minutes!!