from what have understood when i would add bsc in metamak , all the coins would have same address
BSC is trying to increase adoption and attract customers with low fees so think about it and a cheaper version of Ethereum network with the same wallet seed.
this is because account based system.
This does not mean that all tokens on Ethereum network will appear on BSC when you customize your wallet but if there are tokens moved to BSC there will appear there.
if you create a new wallet and generate a new seed will have different address.