How does Continuity and Handoff work and what are the differences?
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