Open-source full Bitcoin client software that utilizes the Qt UI framework for a graphical user interface. Wladimir J. van der Laan developed the software to use the original reference code by Satoshi Nakamoto, but with an improved user interface. Today, it is bundled with the Bitcoin Core client and is collectively maintained by the Bitcoin core developers (who are paid by the Bitcoin Foundation) as well a large community of developers across the world.
Bitcoin-Qt can be downloaded from bitcoin.org and the source code can viewed and contributed to on github.com.
Bitcoin Core
As of version 0.9.0, Bitcoin-Qt was rebranded to Bitcoin Core due to the progress made in separating the client code from the graphical interface. Since the technical specifications of the Bitcoin protocol have not been completely documented, the Bitcoin Core code is considered to be the reference client that defines the Bitcoin protocol. Other Bitcoin clients typically attempt to match its behavior (including any bugs) as to avoid protocol inconsistencies and avoid a hard fork in the blockchain for their users.