Just a correction Dave...
Arguably the biggest difference, as I understand it, between BTC and ETH is that rather than mining Bitcoin, in the ETH blockchain, miners work to earn Ether, which us a token that sort of serves as "gasoline" for the network.
Currently Ethereum does have miners creating ETH blocks on the Ethereum blockchain just like miners do in Bitcoin. They are rewarded for that with with some new ETH. Just like with Bitcoin they are also paid a fee for the transactions embedded in each block. The fee for each transaction is paid for in "gas" but the gas is ETH too. So they both create blocks and get an ETH block reward, and get paid for processing transactions in each block in "gas" aka ETH.
Some blockchains like NEO have a separate coin or token for their "gas", Ethereum does not.
Some people have mentioned that Ethereum is moving to PoS (Proof of Stake) for mining new blocks. This is a stated goal and will remove the very wasteful PoW (Proof of Work) from the picture. This process is already underway with the Casper FFG project which is introducing PoS into Ethereum to validate some blocks, but not all. Eventually only PoS will be used and miners will be replaced with Casper block producers and validators. Except there won't be 30,000 of them, maybe a thousand or two.
Regardless I would say the main differences between Ethereum and Bitcoin are actually:
- Ethereum supports contracts written in a Turing complete programming language (means it can be used to code any program) called Solidity. These contracts have given huge flexibility to Ethereum for developing dApps.
- Faster time to produce blocks which means faster time to process transactions and higher transaction throughout. Compare 20 seconds to 10 minutes for Bitcoin.
- More centralised governance. How Bitcoin evolves is largely controlled by the miners. Some will say that is as it should be in a decentralised system. However miners are reward with Bitcoin therefore they support changes to Bitcoin that will maintain their reward stream. So the main Bitcoin would never make any change like switching away from Proof of Work that eliminates miners.
Meanwhile Ethereum has the Ethereum Foundation supporting it and Vitalik is a huge part of that. Whatever he says has a huge impact. Miners of Ethereum largely go with the flow and seem to accept whatever the foundation says. The notable exception would be Ethereum Classic where a group of miners didn't agree with the fork to "undo" the DAO contract disaster. ETC is still out there but dying out, currently worth 0.038 ETH.