What exactly is the difference between "Key Distribution" and "Key Management"?
Key Distribution. Key distribution is, well, the process of distributing (cryptographic) keys to different parties. Usually this involves mechanisms which are considered "out-of-band", i.e. mechanisms that don't use the later communication channel for the transport of keys. Alternatively key distribution can be done by relying the distribution of new keys upon the safe distribution of old keys, that's what a KDC is doing.
Key management. Key management is, well, the process of managing (cryptographic) keys, the usual meaning implies management over the whole lifetime of the key. Key distribution is a part of key management, but it also includes key generation, key escrow (for backup purposes), key deletion, key revokation, key usage and key trust management. If you want to learn more about key management, the Handbook of Applied Cryptography has an entire chapter devoted to it (PDF).