What was the "curse of the law?"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: Gal 3:13
Is it the same as the "wages of sin?"
This passage that you quoted is found in context of Galatians 3 discussion of the authority of the law:
10 For as many as are of the works of the Law are under a curse; for it is written, “Cursed is everyone who does not abide by all things written in the book of the law, to perform them.” 11 Now that no one is justified by the Law before God is evident; for, “The righteous man shall live by faith.” 12 However, the Law is not of faith; on the contrary, “He who practices them shall live by them.” 13 Christ redeemed us from the curse of the Law, having become a curse for us—for it is written, “Cursed is everyone who hangs on a tree”— 14 in order that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we would receive the promise of the Spirit through faith.
Within that passage is a quote from Deuteronomy 21:
“If a man has committed a sin worthy of death and he is put to death, and you hang him on a tree, his corpse shall not hang all night on the tree, but you shall surely bury him on the same day (for he who is hanged is accursed of God), so that you do not defile your land which the LORD your God gives you as an inheritance."
What ultimately is the apostle pointing out?
That the curse is from the Law, because none have the ability to conform to every aspect and respect of the Law. That Christ became cursed so that the blessedness that came to "us" (the heritage of the apostle) of the seed of Abraham might also come to the Gentiles, too.
People were hung because they were judged to be in violation of the law. Christ was judged as one who violated the law, but the testimony was tainted by extortion and bribery. Christ was in fact "hung" innocent of any violation of the Law, and yet cursed.
It is in this context that one can demonstrate how the Love of God is demonstrated, for the curse was unwarranted yet imposed as Isaiah 53 states - from out perspective it was God's judgment upon Him - Yet, it was God's will that Christ "hung."
What we as humankind view as a curse, God viewed as love, exemplified.