How would you describe the difference between mitzvos and dinim?
How would you describe the difference between halachah and dinim?
A mitzvah is a raw commandment or rabbinic enactment.
Din is a halachic category that something or someone falls in, such as "a Samaritan woman has the din of a Niddah". Or "Shlomo has the din of a mazik and has to pay damages."
Halacha is the accepted way of doing things. It is based on Mitzvah, oral law/interpretations, and customs. It's the polished mitzvah and can differ vastly from the raw mitzvah. For example, we have a mitzvah to cut off the hand of a woman who grabs a ballsack of two men who are fighting. The halacha is that she only pays a monetary fine.
Sometimes halacha refers to a detail of another halacha.