The primary difference between the domains is that they exist on different blockchains.
The domains are built on the Ethereum blockchain, except for the .zil domains which are built on the Zilliqa blockchain.
The domain extensions are fundamentally similar and work for both websites and payments.
Zilliqa has cheaper fees and (on average) faster transaction times, but Ethereum is an older chain with a broader integration of Web3 tools, as well as marketplaces like Opensea and Rarible.
It is important to note that, to the end-user, the underlying blockchain does not significantly change the experience of using the domains. For instance, all domains can be used for accepting payments and issuing censorship-resistant websites.
However, some integrations such as ETHMail and native support for Brave and Opera browsers are not supported for .zil domains.