3 gun nation is an organization that runs several matches across the US and offers a ruleset/affiliation to local clubs so they can run matches using their rules. The main advantage to this is that you can run classifier matches to try and get a sense of how you compare to other shooters using the same stages.
There are many other matches run locally (either major of minor/club level matches) that will use their own rules - but many of the major matches will use rules that are pretty similar (each match will usually have a link to the local/match rules on the main website).
The main differences will relate to:
1) Scoring - commonly it will be straight time (the actual time used to shoot the stage + any added on penalties) or stage points (each stage is worth a certain number of points - fastest adjusted time gets the top points, all others the percentage they had of the top shooter). Most matches require 2 hits on paper target to neutralize and avoid penalties, steel must fall or "flash" as indicated.
2) Divisions - most major matches run your division based on your rifle - "Tactical" divisions use .223 and "Heavy Metal" will be .308, and either Optics (if you have a scope with magnification capability) or Irons (true open sights often, but many matches include red dot sights with no magnification in this category). Most matches also have open division (almost always use of a bipod puts you here, or more that one optical scope), and occasionally trooper class (you have to carry all equipment for the match on you the whole time O_O). Certain pistol and shotgun features will be limited in many matches as well (ie no compensators or optical sights unless in open), and occasionally you will have caliber requirements also (ie, 12 gauge only and pump shotguns only, pistol must be .45 and max 8 round mags in heavy metal).
Obviously, there can often be minor (but sometimes important!) differences based on local range rules or organizer preferences (ie do you need chamber flags, how strict they are on dedicated safe zones, whether you pre-load shotguns as a group or come to the line empty and load there, firearms slung or not, etc).
As for IPSC, it does not have a true 3 gun format as most people in this forum will speak of - using 3 firearm types on the same stage with guns staged/slung. IPSC has the grand tournament format where each stage can only have 1 firearm type (ie pistol, shotgun OR rifle) and the "multigun" function comes from running several stages of each firearm type under that firearms IPSC ruleset and combining the results into a total overall match. I've seen tournaments run with stages intermixed (ie shoot a pistol stage, then a rifle stage, then a shotgun stage, back to a pistol stage, etc) or run as a "pistol match" one day, then a "shotgun match" and "rifle match" on separate dates with the overall scores put together to get a tournament winner.
Personally I love the multiple guns on 1 stage format compared to the IPSC concept. I am member of 3 Gun Nation and they are very good for allowing a standard ruleset that keeps things consistent from match to match, but if you do get into some US matches you'll see that it's still pretty open in the market as to what rules you use - the bottom line is you'll need to read through a few pages to get the key points for each match you shoot. There are quite a few groups in the Southwestern Ontario area running matches, I'd suggest popping out to a match or two to get the feel, but a warning now that once you see it you'll probably be hooked for life!
Enjoy!!!!
lonedrone