How does Continuity and Handoff work and what are the differences? I am trying to understand how the continuity and handoff features work and what is the difference between them. I suppose handoff is for specifically transferring activities from one device to the other while continuity is being able to answer call from mac or reply to messages. Although the difference is quite small. 

So how exactly do these work ? do they use the same multi peer connectivity framework ? And are these only available to devices with the wifi-direct chip ( 4s and above )?
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