Usually, in modern cryptography, the key is randomized within a specific domain. For symmetric encryption, for instance, the key consists of 128 to 256 random bits, which is the minimum number of bits to get (close to) 128 to 256 bits of security. An RSA private key on the other hand is created from 2 or more randomly chosen prime numbers.
For classical ciphers the key space commonly consists of a number of specific symbols making up an alphabet. The English ABC is one of these alphabets. However, unless the password was generated at random, it is still probably best to think of it as a password. The reason for this is that a non-randomly chosen password has less strength than expected from a key of the same size. I'd not be surprised that in the classical sense the term key and password were used interchangeably (but I'm not a historian).
In modern cryptography we have algorithms called password-based key derivation functions (or, more simply, password hashes) that create a key from a password. Those are generally needed to create a more secure key from the password. Of course, if the password is really weak then such a PBKDF can only do so much.
Both passwords and (symmetric) keys can be considered secrets, in case you are looking for a common term. So no, a key is not something entirely different.
