I'm an iOS developer, so I'll help you out here.
There is technically very little difference between an iPad app and an iPhone app. What "differentiates" an iPad app from an iPhone app is really just the size classes that can be displayed and what happens when an app is displayed within those classes. To break it down, there are two size classes "Compact" and "Regular" and two axis, "Vertical" and "Horizontal". Then there is also the orientation "Portrait" or "Landscape".
An iPad app in full screen Landscape is an app that runs in Regular-Regular-Landscape. When this is the case, the app can take advantage of a displayed list view next to a detail view. Or, when in Portrait, can have the list view pop over the detail view. This is because the iPad takes advantage of something the iPhone ignores (except in landscape on an iPhone Plus) called the SplitViewController. (There will be a lot of little exceptions, so let's speak in generalities from here on out.) The iPhone, as I said, ignores this and just displays a list (for example) on one screen then replaces that with the detail view when an item has been selected.
Same app, just works slightly different given the size and device contexts.
When a 12.9" displays two apps side by side in a landscape context, it is essentially displayed two Regular-Regular-Portrait apps in the iPad context. Flip this into Portrait, and they become two Compact-Regular apps and they default to functioning as they would on a Compact-Regular-Portrait device... the iPhone.
The 11" (and 10.5" and 9.7" for that matter) display Compact-Regular-Portrait when side-by-side in landscape always. Even a swipe over window is still Compact-Regular-Portrait, it's just more compact than the compact when two apps share the screen equally.
My hope, of course, was that with the extra screen real estate given to the 11", it would bump up the size classes to be like the 12.9" but, alas, it is still the same as the smaller Pros have been.
This is a long way of saying that, even with the impending iPadOS, the 11" will still display two apps side-by-side in an iPhone-like context but, if they've been built correctly, should still be "proper" iPad apps. But, no, they won't function like they do on the 12.9".
One thing that will be possible though, and this should give you heart if the above was a downer, is that apps that are written to take advantage of it can have their list view and "detail" screen on one side and another detail view side-by-side. They've shown examples of this where you can have your Mail inbox and message displayed and then the compose window, side-by-side so you can refer back to what you were reading or another email or swipe in a new app altogether for whatever the usecase might be. So it's not exactly what you're asking for but it's definitely a power feature that's very un-iPhone-like that I've found to be very cool.