
der Spruch
saying
A short, memorable sentence that contains a piece of life wisdom, a motto, or a joke; a proverb or idiom.
An der Wand hing ein Schild mit dem Spruch: „Carpe Diem“.
On the wall hung a sign with the saying: 'Carpe Diem.'
saying / remark / ruling
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saying
A short, memorable sentence that contains a piece of life wisdom, a motto, or a joke; a proverb or idiom.
An der Wand hing ein Schild mit dem Spruch: „Carpe Diem“.
On the wall hung a sign with the saying: 'Carpe Diem.'

remark
A thoughtless, cheeky, or inappropriate remark.
Für diesen dummen Spruch musste er sich später entschuldigen.
He later had to apologize for that stupid remark.

ruling
In legal language, the official decision or judgment of a court or arbitration court.
Der Spruch des Schiedsrichters ist für beide Parteien bindend.
The arbitrator's ruling is binding for both parties.
'Der Spruch' (saying/remark/ruling) belongs to the word family of 'sprechen' (to speak). A 'Spruch' is therefore something that is said or 'spoken' and often has a special, memorable form.
Kennst du den Spruch „Wer rastet, der rostet“?
Do you know the saying 'Wer rastet, der rostet' (you snooze, you lose / if you rest, you rust)?
The meaning can often be recognized from context. If it is about wisdom or sayings, meaning 1 is intended. In connection with negative adjectives like 'dumm' (stupid) or 'frech' (cheeky), it is meaning 2. In a legal context (court, judgment), it is meaning 3.
Mein Opa kennt viele alte Sprüche.
My grandpa knows many old sayings.
In the colloquial sense of a cheeky remark, there are the fixed expressions 'Sprüche machen' and 'Sprüche klopfen'. Both mean that someone is constantly making funny or inappropriate comments.
Hör auf, immer so dumme Sprüche zu klopfen!
Stop always making such stupid remarks!
The meaning 'Urteil' (judgment) or 'Entscheidung' (decision) is limited to legal language. In everyday speech, 'der Spruch' is never used in this sense.
Nach langer Beratung verkündete der Richter den Spruch.
After lengthy deliberation, the judge announced the ruling.
judgment / verdict
Urteil refers to the court's decision at the end of a trial. Spruch is also an official legal decision, but it sounds more formal and can also come from an arbitration tribunal. Urteil is usually the more common term for a court decision.

Nach dem Schiedsverfahren verkündete das Schiedsgericht seinen Spruch.
After the arbitration proceedings, the arbitration tribunal announced its ruling.
Nach dem Prozess verkündete das Gericht sein Urteil.
After the trial, the court announced its verdict.