I am trying to run a staking pool with these docs. I find that there are signing key and verification key but no private key. I am curious what is the difference between signing key and private key? Can I generate private key from signing key?
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They’re basically the same. If you can sign-off on transactions on your pool using a variety of keys, then you don’t want the public to get hold of those keys, so you want to keep them private. Public keys, on the other hand, cannot be used to sign transactions with.
You want to keep signing keys private. If the key ends in .skey it’s generally a secret key or a key you want to keep private.
It’s just my opinion - if I’m wrong, I’m hoping others will chime in.
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We are using private key to sign transactions, therefore it’s called a signing/secret key
This is a good article by @Cardanians.io about keys and Cryptography:
https://medium.com/@Cardanians_io/cryptography-for-cardano-wallet-users-6b43d989ee8b
The public key is used as an address on which some ADA can be sent. The corresponding paired private key is used to spend the ADA coins from the address. You can imagine that a public key is an account and private key is a password needed to spend coins
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JT you nailed it 
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so
signing-key is the private key
and
verification-key is the public key, and can be derived from the private key?
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