The purpose of keys is to parametrize a cryptographic transformation. The only constraint beyond key space when choosing a key is this purpose, so typically in symmetric encryption there's nothing to prevent choosing the key uniformly at random in the key space, which is what's best to resist attacks.
The purpose of messages is to convey information. They are often chosen under many constraints, depending on application. For example, being encoded in a particular alphabet like ASCII, using words of a spoken language like English, obeying complex semantic rules, meaning what the message author intends. Messages, in the operational sense of that, are thus typically far from random in the message space, understood as all the messages the cryptographic system can encrypt, then decrypt to the original.
There are exceptions to this last statement, though. For example, in textbook RSA encryption $m\mapsto m^e\bmod n$, it's often assumed message $m$ is random in the message space $[0,n)$, because an assumption on that tune is necessary for security. Directly encrypting a meaningful message per textbook RSA could be insecure. An alternative is to choose the above $m$ uniformly at random in the message space, then use it as key of another cryptosystem to encrypt the actual message.
