return to the Ethereum Standards
Source: What exactly is an Ethereum Client
An 'Ethereum client' is a term referring to any node able to parse and verify the blockchain, its smart contracts and everything related. It also allows you/provides interfaces to create transactions and mine blocks which is the key for any blockchain interaction.
There are currently three reference Command Line Interfaces (CLI) implementations available, as you already highlighted:
All clients should work the same, from the user's perspective. They provide the same interfaces and so on. For example, if you launch a DApp or the Ethereum Wallet or a DApp browser instance, it should not note any difference in communicating with the client.
Graphical clients available to the Ethereum core developers are:
Non-official clients implementing the yellow paper specification are: