One example is PayPal. When you deposit fiat into a PayPal account, you get back an asset: a digital and virtual currency that PayPal holds custody over for you.
Another example is a digital gift card, like a $50 voucher for Amazon. The key associated with this card holds value, and in some cases you can even gift and transfer this online.
Another example is a domain name. If you own a valuable domain name like Meta.com, the asset isn’t “money” but it also isn’t worthless or valueless.
Now take a DAI stablecoin, Aave position, or ENS domain. Very much the same as above assets, except that they align more closely with the three aforementioned properties: trustless, permissionless, and decentralized.
In all of these cases we use the term “ownership” but the ownership of dollars in a PayPal account and ownership of DAI tokens in a wallet have very different properties.