I was always pleased with myself when I recognized whether von Amts wegen was to be translated as ex officio or as of (the court’s) own motion.
But I never asked myself why. Recently, someone has asked why!
It seems that the term ex officio is used in more situations in German than in English. Here is the von Beseler/Jacobs-Wüstefeld dictionary of 1991 on von Amts wegen:
ex officio, by virtue of (one’s) office; because of one’s position; officially; proprio motu (Lat.); upon (of its) own motion; upon/of the court’s (own) motion; in ordinary
I think if someone does something by virtue of their office, ex officio works. But if a court comes to a decision, perhaps because it usually deliberates about it, then of its own motion is appropriate.
I looked up both expressions in the big Oxford English Dictionary, but they don’t add anything much to this.
I have one other excellent law dictionary but I don’t speak much Italian so I have never read the introduction, which I am sure is wonderful. I must scan it and run it through DeepL. It is by, Francesco de Franchis, Dizionario Giuridico English-Italian, 1984
He even says where ex officio would not be used in English. It is the bilingual law dictionary every translator wants, but it is in the wrong language.
Di ufficio; si dice, ad es., che il Lord Chancellor (v.) è un giudice della Court of Appeal ex officio, come pure il President della Chancery Division e il Lord Chief Justice. Ma si noti che quando si vuole alludere ad una iniziative di ufficio e ad una istanza di parte si parla, rispettivamente, di suo officio e di its own motion e di at the instance of the parties.