ERC20 -> ETH Network
BEP2 -> Binance Chain -> Binance Network
BEP20 -> Binance Smart Chain (BSC) -> Binance Network
And BNB is coin for binance, just like ETH.
So if you want to sent token between addresses, make sure you send it to the same network otherwise your token will be gone.
Adding some more details
Ethereum network/blockchain -> use: virtual machine -> main token standard ERC20 -> main/native token ETH (Ether)
Binance Chain (BC) network/blockchain -> use: payment transactions -> main token standard BEP2 -> main/native token BNB (Binance Token)
Binance Smart Chain (BSC) network/blockchain -> use: virtual machine -> main token standard BEP20 -> main/native token BNB (Binance Token)
As others have mentioned, Binance Smart Chain (BSC) is basically a copy of Ethereum. Therefore many projects have switched/ported over to BSC to avoid the high transaction fees in Ethereum (ERC20 tokens -> BEP20 tokens). However, for users, it isn't as easy to get some BNB (Binance Token) vs. ETH. Even when you can buy/trade some BNB, sometimes you can only withdraw it to a Binance Chain, not Binance Smart Chain, address. This is important because even though it is (basically) the same token BNB, it is not straightforward to transfer it from one blockchain (BC) to another (BSC). You will need a Binance.com account to do this easily. Otherwise, you need to use Binance Bridge or a wallet that can swap a token across blockchains (not just within a blockchain with the same token standard). You will likely need some BNB on BSC to power transactions (use BNB to pay gas).