I had this question in my mind today and did some research on this topic.
ERC20
Ethereum is very versatile and allows other types of altcoin to be built on top of it (e.g., BAT). ERC20 is this standard. Anything that is fungible and built on Ethereum is using ERC20. If you would like to see what other coins use the ERC20 standard, you can go to the Trezor website. There are literally hundreds of them. You can also view ERC20 coins in your wallets.
ERC721
Anything that is non-fungible (e.g., one of a kind type stuff), is built using the ERC721 standard. These are starting to get very popular. The most common ones are NBA Topshot and Beeple's artwork that sold for $69 million. So far, I'm not aware of any wallet that supports ERC721 so you cannot view your ownership that way.
Let me know if you have any questions or follow-ups. I find this topic very fascinating. If someone knows how ERC20 rewards ETH holders, please share. I don't think someone who trades BAT is actually paying a ETH fee when transacting but I may be wrong.