expression, noun which may take the genitive case particle 'no'
another; different; something else
Used to indicate that something is distinct or separate from what was mentioned or expected. Often appears in the pattern 何か別の〜.
Let's think of another way.
That's a different story.
Compound of 何か (something) and 別 (different, separate). The exact historical derivation is uncertain, but the phrase is conventionally used to mean 'another' or 'something else'.