What is the difference between the permissibility of a man masturbating with his wife's hand and its lawfulness, compared to the impermissibility of him masturbating with his own hand, even though both involve masturbation by hand?

The difference between the two masturbations is clear. The basic principle concerning gratification and satisfying one's sexual urge is prohibition, except for what the Sharia (definition) has permitted, which is limited to one's wife and slave-women. Whoever goes beyond that by masturbation or other forbidden acts is among the transgressors. Imam Shafi'i explicitly stated the impermissibility of masturbation, and Al-Qurtubi held that a person of integrity would shun it due to its debasement. A Muslim must submit to Allah's rulings even if the wisdom behind them is not apparent to him. Rejecting rulings on the pretext of there being no difference between what Allah has permitted and what He has forbidden is the path of the Jews, who said, "Trade is only like usury," whereupon Allah refuted them, saying, "And Allah has permitted trade and forbidden usury."