There is a seed for HD but nondeterministic keychains use a cryptographically secure pseudorandom generator, on Linux it's /dev/random these random numbers are very secure but they come from nowhere and have no relation to each other
HD keys take a secret, concatenate a specific, usually number based string to the end of it, and then hash the joined string of bytes, and that is a new key. The schemes can also I think actually work from a seed that is made from the seed so if one derived secret is leaked the others are not revealed
These kind of keychains can back up a wallet containing hundreds of keys with just 12 or 24 word ciphers.