AirParrot 2 will allow your computer to send Airplay media or screen mirroring to another device. Reflector 2, on the other hand, will receive Airplay media or screen mirroring. These are 2 very different applications.
If you would like to send your computer screen to a Chromecast or Apple TV device, then you will only need AirParrot. In this case, the Chromecast or Apple TV will be receiving what AirParrot sends from your computer. An example of this type of use might be presenting your computer screen onto a larger screen or watching a movie that is stored on your computer through a television connected to a Chromecast or Apple TV.
If you want to display your mobile device on your computer screen, then you would only need Reflector. Supported mobile devices have the ability to send their screens using the built-in AirPlay feature so that only Reflector is needed on the computer in order to receive what these devices are sending. An example of this might be presenting your mobile device to a PC screen or viewing pictures taken from the mobile device on a larger computer monitor.
In the case of sending one computer screen to another computer on the same network, this is where you might want both AirParrot and Reflector. The computer that you wish to send FROM would need AirParrot, while the computer that would RECEIVE and display what is being sent would require Reflector. One example for this type of use might be using a dedicated media PC connected to a television instead of an Apple TV. Other computers using AirParrot could connect to the media PC running Reflector, eliminating the need for another device.
Reflector is also available for Android devices running version 4.1 and later. Reflector for Android receives in the same way that Reflector does on your computer. Sending an iOS device's screen to an Android device would require only Reflector for Android. Sending your computer screen to your Android device would require that the computer use AirParrot to send and that your Android device have Reflector in order to receive.