日曜日 literally means Sunday.
月曜日 literally means Moon Day or Monday.
The names for the days of the week in both Japanese and English come from names of gods in Roman, Greek, Norse, and Germanic mythologies. The Japanese days of the week, such as Wood Day, Water Day, etc., may sound random but they are not. Care was taken to choose Japanese names that correspond to the same gods of mythology that were used to name the days in English.
You may be familiar with the Norse gods Odin and Thor. Odin's Day (Wodin's Day) is Wednesday, with an obvious sound similarity. The Japanese day is 水曜日 or Water Day. Odin in Norse mythology corresponds to Jupiter/Zeus, but in Roman/Greek mythology, Odin was mistakenly thought to correspond to the god Mercury. Mercury is a liquid metal and its symbol is water, so 水曜日 was chosen to represent Wednesday
Thor's Day is Thursday, again with an obvious sound similarity. The Japanese day is 木曜日or Wood Day. Thor represents Jupiter, and 木 represents the planet Jupiter, 木星.
Saturday is Saturn's Day. The Japanese day is 土曜日or earth/soil/dirt day. In Japanese the planet Saturn is 土星.
Friday comes from the Germanic goddess Frigg (Roman goddess Venus). In Japanese 金星 is the goddess Venus, so 金曜日 is used.
Tuesday is named for Tiw (Tiw's Day), a Norse god, but is named for the god and planet Mars in Latin-based languages. In Japanese 火星 is the planet Mars, so 火曜日 is used.
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As was mentioned, the Chinese language does not use these mythology-based names, but uses numbers.
Monday 星期一 "day number one"
Tuesday 星期二 "day number two"
Wednesday 星期三 "day number three"
etc.
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Sources (except for the names of Chinese days of the week):
etc.