Connecting Arduino to android mobile using bluetooth
They will all probably work, some easier than others.

First, a shield is not a cover and is defined at arduino.cc as: "Shields are boards that can be plugged on top of the Arduino PCB extending its capabilities".

This means that shield provides functionalities like, e.g. bluetooth.

The bluetooth modules are similar, but requires different levels of work and programming knowledge. The shields are made to make it easier for people new to programming do some cool projects. I would suggest you follow a tutorial and maybe buy exactly the same module if you feel that you knowledge of C/C++ is at a beginner level.

I myself have several of the $6 module and it is also easy to get started with. You need to connect 4 cables (power, ground, transmit (tx) and receive (rx) and send data via correct UART/Serial line at the default baudrate (9600).

Android will be the device initiating the connection so when you search for available bluetooth devices the shield/module will show up in the list. Once paired you can send/receive data.