Thanks for bringing that up JWS. Some of the most powerful messages in the bible are regarding sonship.
There are other instances where a different "sense" is sometimes applied to sonship:
One example is Gideon, & his "seventy sons," and that other son, Abimelech, who never seems to get counted with the rest.
Gideon had many sons:
Now Gideon had seventy sons who were his direct descendants, for he had many wives. His concubine who was in Shechem also bore him a son, and he named him Abimelech. -Judges 8:30-31
Note that while his concubine "bore him a son," the child was not counted amongst his "sons who were his direct descendants." In other words, the concubine bore a son for him, but the child was not his "son" in the same sense as these "direct descendants" were.
Later, after the death of Gideon, Abimelech goes to the people of Shechem (where his concubine mother was from) and tries to persuade them to follow him instead of the seventy. Listen to how he appeals to them:
And Abimelech the son of Jerubbaal went to Shechem to his mother’s relatives, and spoke to them and to the whole clan of the household of his mother’s father, saying, “Speak, now, in the hearing of all the leaders of Shechem, ‘Which is better for you, that seventy men, all the sons of Jerubbaal, rule over you, or that one man rule over you?’ Also, remember that I am your bone and your flesh.” -Judges 9:1-2
Note that even Abimelech himself does not consider himself part of "all the sons of Jerubbaal." What the example from Abimelech's life shows us is that a "son" in one sense can be excluded from the list of "sons" in another sense. In the case of Abimelech, it was because he was born of a concubine and not by one of Gideon's wives.
Was Ishmael a different kind of "son" than Isaac? It turns out he was, in a number of ways:
Isaac was the "child of promise", Ishmael was the child of disobedience or unbelief. Ishmael was the result of Abraham and mainly Sarah's attempt to force the promises of God to come to pass through their own conniving and willfulness.
Ishmael (like Abimelech,) was born of a concubine, and not by his father's own wife
As a result, it was in Isaac that Abraham's descendants were to be named. (Gen. 21:12)
So, was Ishmael Abraham's son? Yes! In one sense; according to the flesh.
Was Isaac Abraham's "only son"? Yes! In another sense; according to the promise.
I believe that this drama illustrates two powerful truths to the way life works in the universe that God has created:
1. When a person, through their own willfulness tries to force the good things that God has promised to come to pass through their own designs and willfulness, then God allows this, but he also allows that person to be responsible for the results.
Conversely, when a person allows God to work out his promises of good things in a believer's life, then He (God) becomes responsible for the results.
We see a powerful testimony to this truth of what happens when believers take matters into their own hands with the Arab / Israeli conflict in the Middle East today - the descendants of the child of obedience (promise/faith through Issac) and the child of disobedience - (willfulness though Ishmael)
2. Sonship with God does not come by way of our works, church affiliation, intelligence, etc., but only by faith.
Abraham's "only son" came by his only wife, according to God's only promise, and thus, it was only in Isaac that Abraham's descendants would be named.
Paul brings this theme to a conclusion in Galatians 3:
Know ye therefore that they which are of faith, the same are the children of Abraham. 8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. 9 So then they which be of faith are blessed with faithful Abraham. 10 For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them. 11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith. 12 And the law is not of faith: but, The man that doeth them shall live in them. 13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree: