כִּֽי־עָ֭שִׂיתָ מִשְׁפָּטִ֣י וְדִינִ֑י יָשַׁ֥בְתָּ לְ֝כִסֵּ֗א שׁוֹפֵ֥ט צֶֽדֶק
kiyʿosiyso mishpotiy vediyniy yoshavto lechisseyʾ shofeyt tzedek
For You have upheld my right and claim; You sat on the throne, O Judge of righteousness.
1.....(9.7)
You have maintained my right and my cause;
Rabbi Joshua in the name of Rabbi Idi, interpreted this verse as follows, The congregation of Israel said to God: "Master of the universe, I confess my guilt, for I am soiled with the filth of the wicked deeds I have done, but the nations of the earth are also guilty in that they crush and inslave me". Likewise another verse says, I will bear indignation of the LORD (Michah 7:9). Why? Because I have sinned against Him. Yet, He will plead my cause against the nations of the earth.
1.
...my judgment and my cause:
Heb. משפטי ודיני, words doubled in Scripture, for there is no difference between them
1.
...You sat on the throne...
The throne of judgment.
1.
For You have maintained my right and my cause:
You have fought for me, for it was a great miracle that the stone reached his forehead, as he was altogether clad in iron; and it found an exposed place in his forehead.
1.
I will acknowledge the LORD in every mood of my heart;
[אוֹדֶ֣ה] (ODEH)
Denotes a strong and vigorous expression of our thoughts and feelings as regards a thing or a person, thus, primarily, “to acknowledge.”
(ODEH ... LIBBIY)
is to disclose to someone the feelings which we have for him in our hearts, “to thank” and “to do homage”.
Used here in reference to God, means “to acknowledge God”, to proclaim the awareness and recognition of His existence, "with all my emotions, with every mood of my heart, joyous or sorrowful,” says Israel, “I shall strive to attain clarity as regards God, and I shall proclaim the recognition of God which I shall thus gain.”
“I wish to proclaim all the acts of Your rule which are manifestations of Your direct intervention in the course of history”. These acts are particularly the great miracles that occurred when Israel first became a nation and which revealed the greatness of God.
מִשְׁפָט
FROM KLEIN DICTIONARY:
m.n. 1 judgment. 2 seat of judgment. 3 cause, case, suit. 4 sentence. 5 justice, right. 6 ordinance. 7 decision. 8 due. 9 privilege.
[Formed from שׁפט (= to judge), with pref. מִ◌.]
מִשְׁפָּטִי adj. MH judicial, legal, lawful. [Formed from מִשֽׁפָּט with suff. ◌ִי.]
דִּין
FROM KLEIN DICTIONARY:
m.n. 1 judgment. 2 verdict, sentence. 3 lawsuit, cause. 4 law. PBH 5 logical deduction. [From דִּין. cp. שַׁדּוּן.]
The following is from an article -
Malbim Dictionary Definitions: The Differences between Hebrew Words for "Judgement" & "Law"...
http://www.myrtlerising.com/blog/malbim-dictionary-definitions-the-differences-between-hebrew-words-for-judgement-law-remember
Din (often translated as "judgement") means hearing out the claims & accusations.
It's basically the judicial proceedings.
In connection to that idea, din often means "consequences," whether positive or negative.
We often speak of harsh din or sweetened din—meaning that the claims, accusations, and consequences end up harsh or sweetened.
Mishpat (often translated as "judgement" or "law" or "ordinance" or "statue") is the conclusion of the din.
In other words, mishpat is the verdict. (Or, in the case of its verb shafat, the act of reaching the verdict.)
Its root is shafat--שפט—often translated as "judged."
Shofet--שופט—is "a judge."
Mishpat also means the person-to-person (bein adam l'chavero) laws.
The reasoning behind a mishpat is understandable to the human mind (as opposed to chok, a law in which its reason is not comprehensible).
This is why, in Tehillim for example, different kinds of mishpatim are mentioned.
Note: All the definitions come from Malbim.