In Electrum:
- You're sending all your addresses (until the gap limit) to a public server.
- This server then checks for every TXO that matches with one of the addresses.
- Once this search is done, it returns you the transactions associated with these addresses.
- When spending bitcoin, you reveal to them information like which UTXO is being spent, how much money is transferred, and to whom.
In Feather:
- You're requesting from a public server to send you the blockchain in sequential order, starting from the latest block until the wallet's block height (or block 1, if you've lost it).
- For every transaction received, you check if it belongs to you, utilizing the technology of stealth addresses. If you do not, you discard it.
- When spending monero, you don't reveal neither which output is being spent, neither how much money is transferred, nor to whom (to which address).
The big problem is, obviously, scalability. Feather is a lightweight wallet and you're requested to download the blockchain. Not so lightweight if you've lost the wallet's block height!