What's the concept behind ethereum transactions that allows them not to require change addresses? What's the underlying difference compared to - for example - bitcoin?
The fundamental difference between Ethereum and Bitcoin is that while Bitcoin uses a UTXO model, Ethereum uses a state-transition model.
In Bitcoin, in order for a transaction to be valid, it must point to a set of Unspent Transaction Outputs, which then become the inputs for that transaction. The output value of the transaction must equal the sum of the inputs, so there will generally be change, which is deposited into a change account.
In Ethereum, every account simply has a balance, which increases when it recieves transactions, and decreases when it sends transactions. There is no need for change addresses, because all transactions simply deduct from one account and add to another, without needing to reference old transactions or spend quantized amounts.
Change addresses are a privacy feature, not a bug.
The idea is users would choose a different change address for each transaction. Someone analyzing the blockchain would then not be able to tell which address was the receivers, and which was the change.
In reality, most wallets do not use change addresses in this manner. When a user buys something, the change is automatically returned to their original address.
Ethereum developers decided the privacy potential of change addresses were not worth the additional complexity they required. Possibly, they foresaw on-chain trustless mixers as a viable and more scalable alternative.
Creating a change address may also increase security as it decreases the number of publicly available signed messages made by one address https://www.reddit.com/r/Bitcoin/comments/3euuka/still_confusedwhy_is_it_not_secure_to_reuse/