@Gibsalot i might be in over my head (or more likely get on a tangent) and fail to answer the question. but here goes-
burst wallet basically has a block explorer built in and that is what is displaying all the info. the standard bitcoin wallet does not keep a lot of chain data, in order to save space and time it pulls out for quick access/display what pertains to addresses in it's wallet. there is software for bitcoin chain to do similar things such as bitcore (which is modified to store more info to be rapidly displayed) with insight explorer, colored coins for assets and pay to scripts (on a tangent and over my head here).
now regarding a wallet.dat file, here is a link about what it contains https://en.bitcoin.it/wiki/Wallet
a lot of that (account balance, account transactions) is stored there so it doesn't have to rescan the chain when it is asked for it (and doesn't keep it for all addresses because of space and time). but notice the keypairs for multiple address and key pool for future address which indicates that a single bitcoin wallet is meant to handle (and use) many addresses and key pairs. key pair is private/public key encryption which (as you probably know) means one creates an address and signs transactions using the private and other people verify with the public. in burst your password is your private key (well it gets hashed once first), in bitcoin wallet it creates a private key and stores it in the wallet. one could create (or um... borrow?) a private key and import it into the bitcoin wallet for the same effect. fundamentally all the data is there on the blockchain but the software does not pull it out to quickly display unless it is holding the key pair.
i hope that helps (and i hope i got the facts right).
edit: additionally look at info on brainwallets for bitcoin https://en.bitcoin.it/wiki/Brainwallet