I have the iPhone 6 and the note 4.....
The iPhone is smooth and fluid because it does basically nothing except run apps. What it does do, it does well but doing 1 thing at a time isn't hard on the hardware.
Not exactly. iOS is an OS, just like anything else, and yes it runs applications, just like Android, Windows Phone, BlackBerry, etc. Multitasking is similar on both iOS and Android as well, in the sense that it's "multitasking". That being said, I can run background tasks on both platforms and they behave the same. And this isn't the place to give a lesson on multitasking on each platform so I'll skip it.
The iPhone, while running on 1GB RAM is just more efficient. The apps are well behaved, and this is intentional as Apple restricts certain things from developers, which isn't always a bad thing. Android is fluid and smooth as well, on a non-skinned device like a Nexus. It's things like TouchWiz, or LG's skin that causes the stutter and lag.
My S5 lags and stutters, but my M8 is smooth/fast. The Note 4 just stutters; it's just the way it is. If you've never used an iPhone or Nexus (or even the Moto X) you won't notice it because you're used to it.