Giving an example regarding the principle that actions are by intentions

The Shaykh : Some commentators cite the hadith of intention mentioned earlier as an example of two men. One of them traveled for his business affairs, and when he returned to his home at night and went to his bed, thinking his wife was in it, he lay with her and had intercourse with her. But when morning came and it became clear, the woman was not his wife; rather, it was another woman, perhaps a relative of his wife, who had come to stay because of circumstances that arose during the man's absence. His wife had gone to her family's house, and her sister or neighbor had come and stayed in his house. This is not considered adultery because actions are by intentions. He came to his house and lay with his bed, so he bears no sin.
The other man is one who is accustomed to committing fornication. So when night fell, he went out looking for a target. When he entered the dark room and had intercourse with the woman there, and then the light was turned on, it turned out that the woman was his wife. She had gone out with the same intention when he went out; he went out for fornication, and she went out for fornication. Then fornication brought them together on the same bed, and each was unaware of the other. They are equal in sin, even though they were originally a married couple. However, since the intention of each was adultery, each is considered an adulterer, and it is not considered that he satisfied his desire with his wife, even though in reality he did satisfy his desire with his wife. The act is the same, but the intention differed. From this standpoint, it is obligatory for anyone who is afflicted with a religious duty for which a reward has been arranged, whether this arrangement is from the state or from an individual, that this arrangement of money for the man does not change his intention or his sincerity in obeying his Lord, Mighty and Majestic. This is what can be said for now.