So the Netziv in Ha'amek Davar explains Mitzvos as being:
נכלל בזה מ״ע ול״ת שבתורה שבכתב וגם המשנה היינו קבלות בהלכות פסוקות המכונה בשם צווי כ״פ
So they include the positive and negative commandments that are in the Written Torah as well as the Mishnah that are received as halachos and posed in the format of commands.
On Chukim he says:
אלו כללי התורה איך לדרוש ולחדש מה שלא נאמר בפירוש
These are the rules of the Torah how to expound and provide novel insight for that which is not explicitly stated
Mishpatim are generally regarded as social or civil laws.
Refer to Sforno on the opening of Parshas Mishpatim 21:1 which also helps provide further clarity of the breakdown:
ואלה המשפטים, in the previous paragraph the Torah spoke about the prohibition of coveting property belonging to someone else (20,13). This did not involve action; by contrast ואלה המשפטים, now the Torah speaks about laws governing the concrete nature of “אשר לרעך,” tangible matters belonging to your fellow man. (Sefaria translation)