This is an astute summary. Yes, it is misleading, but such is the way of language growth: when transferring concepts from one language to another, sometimes meaning is permanently mutated or lost.
Consider French "journée" and English "journey". The English word is a direct loanword from French, but in French it means "day" or "a day's work" and in English it means "a set amount of travelling". The etymology is fairly natural, but the English word only captures a fragment of the French meaning.
I think the analogy applies to monads as well: the word denotes/connotes something significantly different in Haskell than in mathematics. It's just the way it is. When learning Haskell, if you already know category theory you can use this knowledge to ease your understanding of the Haskell concept, but it's not a direct translation.