Xamarin SQLite PCL implementation
The SQLite PCL package that is used by the Xamarin Forms example uses SQLite.Net. The Tasky Portable project is using SQLite. The difference is the SQLite.Net is a wrapper over SQLite. You use SQLite.Net as an ORM and not not worry about the implementation details. Instead you can create your POCOs in your PCL and decorate them with the appropriate attributes. The Tasky Portable project is just an older way of doing things in a PCL. Now you have the newer way of doing things with SQLite.Net.
Xamarin Forms is not a prerequisite or co-requisite for using SQLite.Net.