Both due and owe have been in the language for a very long time.
Due came into English from French in the 15th century. The French word it came from was the Latin verb debitum that gives us the word debt, “that which is owed.”
As a noun, either singular or plural, due can mean “that which is owing.” One can pay one’s dues literally, as to a club, or figuratively, in the sense of working to get ahead in a profession, as in the headline “Ricky Gervais and David Chang Have Paid Their Dues.”
The expression “to give a man his due,” means “to acknowledge a person’s merits, to do justice to a person.” The expression “to give the Devil his due,” means to give justice to a person for his merits even if he’s otherwise despicable, or if you don’t like him.
As an adjective, due means “payable as a debt.” For example, “The mortgage payment is due tomorrow.” An expression that has been in the language since Chaucer’s day is “in due time” in the sense of “when sufficient time has passed”: “In due time everyone will know what happened.”
Owe, in the sense of “possess” or “own” comes from a Germanic source. In some English dialects the word retains the meaning of ownership, but in standard English, the meaning has gone from the sense of “to possess” to that of “to be obliged to pay”; “Don’t forget the twenty dollars you owe me.”
A similar word of Germanic origin that does retain the meaning of possession in modern English is own.
As a verb, own means “to possess”: “He owns the bakery.” As an adjective, it follows a noun or pronoun: “Alfred’s own son was taken hostage.” As a pronoun, it follows a possessive: “The boy was given a horse of his own.”
No doubt this discussion of due and owe will put some readers in mind of the debate that often arises regarding the proper distinction between the phrases “due to” and “owing to.”
Refresher: Those who argue for a distinction between “due to” and “owing to” insist that “due to” is an adjective and “owing to” is adverbial. According to this position, it’s all right to say “He was late owing to an accident,” because “owing to an accident” tells why. “Due to” must be attached to a noun: “An accident due to carelessness made him late.”
As far as general usage is concerned, the debate has become as futile as tussles over ending sentences with prepositions or splitting infinitives.
According to the Penguin Writer’s Manual, not even grammarians can give a grammatical reason for insisting on the distinction:
Most modern authorities recommend that the rule should be remembered, while acknowledging that its grammatical basis is shaky (there is no reason why “due to” should not be seen as a compound preposition if “owing to” is one) and that “due to” is so frequently used in the sense of “because of” that many modern dictionaries show it with that sense.
The “due to/owing to” distinction is one of those things that people who feel strongly about it should observe without berating others for ignoring it.