Ether is the cryptocurrency of the Ethereum Blockchain. It is a necessary element -- a fuel -- for operating the distributed application platform Ethereum. It is a form of payment made by the clients of the platform to the machines executing the requested operations. To put it another way, ether is the incentive ensuring that developers write quality applications (wasteful code costs more), and that the network remains healthy (people are compensated for their contributed resources).
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Gas is the internal pricing for running a transaction or contract in Ethereum. The term Gas is simply the Ether cost you have to pay to get your Ethereum message or transaction executed as soon as possible. With Ethereum, there is a blocksize limit too – so you’re paying for premium space in the next block.