The means for the end.

Ethereum is frequently compared to Bitcoin, due to the similar type of consensus, the Proof of Work, but differs actually for its aim, that led Ethereum to create from the start a variant of the Proof of Work.
Reading and searching for information on the internet, frequently one finds comments and opinions that generate hype about “Bitcoin is better than Ethereum” or “Ethereum is better than Bitcoin” as for other blockchains or cryptocurrencies. However, analyzing the blockchain world, what matters is “choosing the better fitting blockchain for the scope that one wants to reach”. That’s why Ethereum, in this case, differentiates from Bitcoin or others.
Bitcoin substantially is oriented to coins, while Ethereum is focused on the creation of a decentralized system that enables users to build the famous “Dapps” (Decentralized Apps), based on Smart Contracts structure.
Ethereum does have its coin, Ether, but it was created as the means for the end, allowing to create and use SmartContracts and Dapps, rewarding the parts of the system.
Proof of Work: Ethash.
Let’s start from the basis: what brings together Bitcoin and Ethereum is the use of the same consensus system. Both use the Proof of Work. However, from here, Ethereum develops a version of PoW based on a function called Ethash.
Ethash aims at solving the problem of mining centralization. Few miners groups, or “mining pools” acquire an enormous computing power compared to the rest of actors operating on the network, at the point that these are capable of altering the goodness of the system itself.
Technically speaking, with Ethash, developers aimed to create an ASIC resistant network: ASIC is the term used to identify hardware customized to satisfy a determined function. The whole “integrated circuits” used by miners to mine Litecoin or Bitcoin, to cite the two most famous PoW-based cryptocurrencies, can be described as ASIC since these are customized to reach a scope, at the point of not being available or buildable through the classic commercial lines of computer shops.
One has to remember that, technically, cryptocurrencies based on PoW can be mined using every personal computer. However, nowadays who does this has a percentage of success close to zero, considering that almost every “professional” miner shall have in place way more elaborated and performing systems, creating “mining pools”, or a “set of computers that put together their computational power to compete as one”.
Ethereum objective with Ethash is to create a mining system embeddable on common hardware.
Deepening the possible scopes of this strategy carried out by Ethereum, one can observe how the GPU market is continuously growing.
Ethash exploits this situation: the system uses with both hands the computing power of GPUs. CPUs (processors) are built to work on a calculation system that differs from the one of GPUs (video card processors). In the PoW system built by Ethereum, GPUs perform way better in solving those kinds of calculations, without going into the details here.
Ethereum: Smart Contracts and Dapps.
The classic Proof of Work, customized as Ethash, adding Smart contracts and Dapps, basically lead to the creation of Ethereum.
Deepening the research, we’ll learn that Ethereum constitutes of a vast network of computers. Their job is elaborating transactions and creating, and maintaining, the ledger (blockchain).
We then find “Solidity“, that is the programming language that developers can use in blockchain to create and automatically run the software that we call Smart Contract.
Lastly, we have applications that use the network mentioned above to offer users services like governance, ID managing, and so on. The peculiarity of these Dapps is that by being decentralized, they can’t be simply shut down.
Adding Smart Contracts required the creation of a custom environment, to allow processing and implementing of Smart Contracts themselves.
The Gas.
This environment is called Ethereum Virtual Machine or EVM. As the name suggests, it is a virtual machine installed on every node in the network, by nodes themselves. This is crucial since Smart Contracts and Dapps need to allocate computing resources, a process handled by EVM.
By allowing the whole consensus system to work, EVM needs a price to pay for the computational work: it is called GAS, a price limit (GAS) consumable to reward miners.
Mining is the element that simultaneously brings together and pushes away Bitcoin and Ethereum. Being based on Proof of Work is composed of the same set of actions carried out to create blocks and securing transactions.
The puzzle.
The difference is in the amount of time needed to carry out the “computational puzzle“. For Bitcoin, the puzzle is complicated enough that is solved and accepted by the network in 10 minutes; for Ethereum, the puzzle is complicated enough that is solved and accepted by the network in 15 seconds.
As it happens with Bitcoin, Ethereum continuously adapts the difficulty level of the puzzle. It happens when it sees that the process needs too much, too little, time to be carried out, keeping it around 15 seconds.
A programmed evolution: Proof of Stake.
It is crucial to highlight that the creators of Ethereum plan to shift from PoW or PoS (Proof of Stake) because they think that a blockchain system based on PoS can fit better the needs and objectives of Ethereum.
The transition to the new consensus is scheduled and will be a significant change for Ethereum.