yes, you are totally right this is why I shouldn't write my first review at 3am haha. The EOS tokens where ERC20 tokens on the Ethereum network. However, now EOS switched over from the Ethereum blockchain to its own mainnet, tokens have been replaced with EOS coins issued on the EOS network.
The ERC20 EOS tokens have been frozen on the Ethereum blockchain before the launch of the mainnet.
If you keep your EOS tokens on an exchange, the process is slightly different. The exchange may support the token swap and handle the process for you. I personally sent all mine to binance as they handle this process for you.
Anyway, this has already happened and EOS you are buying now are EOS tokens on the EOS network :) youe EOS tokens allow you to vote on who gets to mine/validate and will be used to have processing bandwith on the network if required