There are certainly a chunk of NFTs that the media only exists on one centralized server somewhere. Someone forgets to pay the bill and poof there goes your art. You can download the image but the contract's `tokenUri` function still points to that old location.
Then the next tier up would store their media on IPFS, if you purchase the NFT you're expected to be responsible for pinning that IPFS content somewhere. That's not communicated too well though. The benefit there is if the original minter stops paying for IPFS hosting but you still have yours pinned, it's still available. I think most of the "Mint as a service" platforms will use IPFS by default.
Then there are projects that are storing the images entirely on chain. These are obviously more costly to create but don't require another service/protocol/platform.
I had always read this as a metaphorical memo. Not necessarily that every team must have a software service running somewhere in infrastructure serving RESTful routes but rather as a way of thinking about agreements between groups. Your team's "API" could be documents describing: if you want us to do XYZ, send us a request via ABC, and you should expect a response in UVW format in x amount of time.
Then the next tier up would store their media on IPFS, if you purchase the NFT you're expected to be responsible for pinning that IPFS content somewhere. That's not communicated too well though. The benefit there is if the original minter stops paying for IPFS hosting but you still have yours pinned, it's still available. I think most of the "Mint as a service" platforms will use IPFS by default.
Then there are projects that are storing the images entirely on chain. These are obviously more costly to create but don't require another service/protocol/platform.