In 2018, there were two available versions of the mobile app. The classic was discontinued in December 2020, even though it still has some features that the newer app does not have.
It’s easy to tell the difference: they had different logos.
If you were directed to this FAQ so that you could figure out which version of the mobile app a forum post was referring to this is as far as you need to read. 
The remainder is more for experienced members of the forum and covers how we as a community are dealing with the ever-changing terminology the platform has presented. But feel free to skip it if you’re not interested in that kind of thing. 
Jargon and History
Note that the name of the 2018 app changed multiple times since it was first released. As of July 2019 it changed again, and after that was just called “SmartThings.“ But with the same picture logo as shown above.
Unfortunately, a lot of the documentation, including the app descriptions, hasn’t all been updated and there is official documentation which still calls the classic app “our new app.“
That means there are forum posts from 2015 through 2017 referring to “the new app“ which are really talking about the one that is now called “the classic app.“ It can get very confusing 
What to call the apps in forum posts?
We’ve tried coming up with abbreviations and nicknames and stuff like that since “smartthings (Samsung connect)“ was released in April 2018, but none of them have stuck.
So one year on, when “new“ isn’t quite so new, we’re going to try something else.
2013
The original version of the app had a lot of “hello, home“ verbiage and came out when the V1 hub was released. So we’re going to call that the V1 app or the 2013 app.
2015
Then when the V2 hub came out in the fall of 2015, A new version of the app was released. It introduced smart home monitor, smart lighting, rooms, and routines. At the time that it was released it was called the new app. Later on it was called the classic app. It went through a lot of versions over the four years since it was first released, and in particular the icons and their names at the bottom of the screen changed multiple times, but you can see they’re all related.
in this forum, just for shorthand and to futureproof posts, let’s call it the Classic app or the 2015 app.
2018
In 2018, the V3 hub was released, and a new app came out from a new UI development team. Originally they tried just calling it “SmartThings” and re-naming the Classic app to “SmartThings classic.” But after about six weeks they changed the name in the App Store of the newer app to be “SmartThings (Samsung Connect).” So you will see support referring to it both of these ways.
In addition, people on the smartthings engineering staff sometimes call it “the One app“ because of internal company discussions about combining all of the various Samsung apps into one. However, in my experience the people working the support line don’t know that terminology, and it can be really confusing to people who have never used more than one Samsung app.
In the forum we tried using the abbreviation STSC, but it didn’t really catch on. So let’s just call this one the V3 app or the 2018 app. It came out in 2018 when the V3 hub came out. It looks very different from the 2015 app, and includes its own if/then rules engine. And a picture of a plant.
2020: the 2015 Classic app is retired, and everyone has to use the 2018 V3 app
So if you are searching the forums and you see something that refers to “the new app,” check the date. If the post went up between 2015 and early 2018, it’s probably referring to the 2015 Classic app. Not the V3 app, since that was not released until 2018.
And if the post was dated after May 2021, it might be referring to the 2018 app OR to the 2021 app. Which is why using the year specification is helpful.
2021: Coming Soon
In June 2021 SmartThings Will release a new version of the app with a very different UI. In the forum, we can just call this the 2021 app.
Apple users will remain on the 2018 app for awhile, though.
NOT a SmartApp
Also, note that none of these is a “smartapp.” SmartApp is a term that applies to code that runs on the SmartThings platform. Not the mobile app that runs on your phone.