My understanding of allegory is that there is a hidden meaning in the text. Consider, for example, Origen's allegorical explanation of Genesis 24:
Rebecca, which means "patience," when she saw the servant and contemplated the prophetic word "puts the pitcher down" from her shoulder (Gen. 24:18). For she puts down the exalted arrogance of Greek eloquence and, stooping down to the lowly and simple prophetic word, says, "Drink, and I will also give your camels a drink" (Gen. 24:14)...
A soul who does all things patiently, who is eager and is undergirded with so much learning, who has been accustomed to draw streams of knowledge from the depth, can herself be united in marriage with Christ.
Unless, therefore, you come daily to the wells, unless you daily draw water, not only you will not be able to give a drink to others, but you yourself also will suffer a thirst for the word of God (Amos 8:11).
In Origen's allegory, the word of God isn't explicitly mentioned. In fact, it's not even implicit; it is hidden. Yet as far as Origen is concerned, this is one of the meanings of the text and what God intended for it to teach us.
Contrast that to Mark 2 and Jesus' use of 1 Samuel 21:
He answered, "Have you never read what David did when he and his companions were hungry and in need? In the days of Abiathar the high priest, he entered the house of God and ate the consecrated bread, which is lawful only for priests to eat. And he also gave some to his companions."
Then he said to them, “The Sabbath was made for man, not man for the Sabbath.
Everything Jesus mentions in verses 25-26 is explicit in the text. Jesus draws a principle from the text, but it is a principle based on a literal understanding (David is David, the bread is bread, etc...) of the text rather than on an allegorical understanding (the well is the word of God, the pitcher is the exalted arrogance of Greek eloquence, etc...) of the text as in Origen's account.
Not sure if this answers your meta question of how we go about defining such terms, but I think here the important thing is how the questioner defines the terms. In this case, I interpreted his question based on my idea of Bob Jones's use of John 5:39 in his own hermeneutic.