The verse you mention regarding God's commandments and judgments states the following. Deuteronomy 6 says, "Now this is the commandment [Hebrew: mitsvah], and these are the statutes [Hebrew: choq ] and judgments [Hebrew: mishpat] which the Lord your God has commanded . . . " (verses 6:1 - 2).
The Old Testament uses various names to refer to different parts of God's law. There does exist a bit of an overlap between what is considered commandments, judgments or statutes. In Genesis 26:5 the Lord said that He blessed Abraham because he "obeyed My voice and kept My charge, My commandments, My statutes, and My laws" (Genesis 26:5, HBFV).
Some naturally wonder about what are the differences between commandments, judgments and alike. Vine's dictionary states the word choq or statutes can also refer to nature's laws (see Jeremiah 5:22, 24, 33:25). It can additionally refer to that which is allocated or apportioned to a person (Leviticus 7:36, Exodus 29:28).
Vine's also states that statutes can reference a law relating to a festival or even a ritual (see Exodus 12:14) or Feast Days such as the Feast of Tabernacles (see Leviticus 23:41). Wilson's Old Testament Word Studies says a statute is, "something decreed, prescribed; a statute, ordinance, law; usually applied to the positive statutes appointed by Moses, the institutions of his religion and civil polity." (page 417).
The meaning of the Hebrew word mishpat is "judgments or rights." It can reference someone who sits to hear a case like a judge and who ultimately renders a verdict.
In reference to the rights of someone (Exodus 23:6), there are several related meanings to mishpat according to Vine's. It can refer to the area in which things remain in a proper relationship to someone's claim (Genesis 18:19), a judicial verdict (Deuteronomy 17:9), and an established ordinance (Exodus 21:1).
Wilson's Word Studies makes an interesting comment about the word mishpat translated as judgments. It states the following regarding this word.
"There is a considerable difference between this word and [another Hebrew word], the former being much more general. Jeremiah 10:24, 'correct me, but with judgment,' as a just as well as a considerate judge. The latter rather implies a settlement of right between two persons, as to what is due to one or both; if Jeremiah had used this word, he would have prayed God to correct him according to his desserts [i.e., what he deserves]."
Biblical examples
Biblical examples of judgments include how to apply God's commandments concerning inheritance when a man has only daughters (Numbers 27:1 - 11, 36:1 - 12). The decision that was arrived at was used as a model for future cases. In principle, this is rather like how English common law operates, in which prior decisions by judges should be normally respected by future judges as precedents to follow.
The difference in the case of the daughters, however, is that God made the initial decision when the situation was brought to His attention. The ultimate judgment was not based on a human trying to figure out what is right according to tradition or human reason.
The Hebrew word translated "commandment," which is mitsvah, normally appears when God Himself directly gives the order in question. It is not used often to refer to what human kings or others in authority order or tell others to do.
The plural of mitsvah often refers to a "body of laws" which are given by divine revelation, according to Vine's. According to Wilson's this Hebrew word means, "to set up, to put, to place; to constitute, appoint; to command, to charge. . . . With an [accusative, or a word meaning "to" someone or something] of person, without mention of the thing commanded . . . " (page 87).
An interesting comment by the (liberal) Interpreter's Commentary is that Deuteronomy 6:1 - 3 is (another) introduction to the law. It, therefore, makes sense it would mention the different parts or sections (judgments) of God's law.