I don't believe there are any software differences at all between an iPad mini and an iPad 2 or iPad Air. Both iPad minis use the exact same display resolution as their larger counterparts (1024x768 non-retina, 2048x1536 retina), just on a physically smaller screen. The whole purpose of this is to ensure that all existing software works identically on both device sizes.
In fact, I don't think it's even possible for an app to "know" which size device it's running on, since there's no technical way to differentiate them. Apple's own iOS Simulator doesn't even list the iPad mini as a separate device to simulate: the only options are iPad (meaning 1024x768) and iPad Retina (meaning 2048x1536).
Ok, so the problem here was that somehow my iPhone was connected to iCloud... But it wasn't at the same time... This is really weird, and Apple should at least notify on this somehow, because my iPhone was connected to iCloud and synced. Wow.
Worked the same for me, though also required e) after a) to d):
a) going to the apple discussions (as mentioned) to 'register' my device(s) with my apple id. (weird)
b) turning iMessages off and on (on both devices)
c) turning my icloud off and on (on both devices) (scary dialog boxes, push on)
d) turning by bluetooth off and on (on both devices)
and finally, after none of that worked,
e) turning both devices off and on.
Presto, it finally worked. The feature only seems to work if the email or message or calendar (whatever you want to hand-off) is actually open on the screen on one of the devices. Unlock other device and the email or messages or whatever icon appears bottom left. Swipe it up and roll.
I have had a few of these issues with icloud and apple id's. Seems like you really have to reset all icloud and messages services to get hand-off working properly.
Best Answer
I can't embellish on the technical aspects of Continuity and Handoff beyond the WWDC bullet points, but I'll do my best to answer.
"Continuity" is the name of the new feature-set included in OS X 10.10 (Yosemite) and iOS 8 to allow more seamless integration with devices.
"Handoff" is the name of a specific feature in which a task started on one device can be picked up - or handed off - to another device to finish or continue.
Continuity also includes features such as phone call and SMS relaying as well as Instant Hotspot.
And yes - these features will not only work between OS X and iOS devices, but two or more iOS devices as well; Just today I accepted a call on my iPad. All of this is done with Bluetooth, and only devices with Bluetooth 4.0 can utilize them.
And for your technical question (which is above my head at this point in time) can most likely be answered here:
https://developer.apple.com/library/ios/documentation/UserExperience/Conceptual/Handoff/HandoffFundamentals/HandoffFundamentals.html#//apple_ref/doc/uid/TP40014338