How do new imported wallets recover the current state?

Wait 5 sec.

There are basically two ways of knowing which outputs a wallet has:They can check block by block since the genesis or a specific wallet's birthday and check if they are the owners of the UTXOs being created and spent. This way they can know not only the current state of the wallet but also the history of it.Checking the current UTXOset and looking if any of the outputs there are owned by the wallet.My question is, what approach do wallets normally take? I know that many take the first one as they allow you to load the historic, but do they also check the UTXO set? Are there wallets that only check the UTXO set and don't allow you to check the historic?