How do private keys in Bitcoin-Qt's encrypted wallet differ from BIP38 private keys?
BIP38 provides a standard to create encrypted paperwallets (or physical coins in the case of Mike Caldwell). Bitcoin Core is wallet software which stores its most sensitive information in an encrypted format to protect against theft. 

When you export a private key from Bitcoin Core, you're essentially doing the same as when you decrypt a BIP38 paperwallet: You're making the actual private key available in plain text. Obviously, the actual private key can be used to make a payment with associated balances.