What is the difference between seed phrase and private key?
The seed phrase is a 12 word that can be used to get your private key while the private key is derived from your seed phrase. If your seed phrase is multiwallet like trust wallet then you can used it to get your private key from each network like eth, btc. Basically, your seed phrase is like original and the private key is the clone if you put it that way and both can access the wallet.
That's a bad analogy. Seed is like a plant seed that you can plant and get a tree with a lot of branches. It can have different sizes but has to provide the same strength as the private keys that you want to derive from it which is 128 bit hence the 12 word minimum but it can have different word counts (ie. entropy sizes).
The key that you derive is just a number that can be used in any asymmetric cryptography algorithm granted it is in valid range. So can use a single key as bitcoin, litecoin, ethereum,... key. You don't need to have a special seed.