Explaining the Shari`ah-based rulings on male secretions, the late Sheikh SayyedSabiq states in his well-known book, FiqhAs-Sunnah:

Wadi: It is a thick white secretion discharged (by some people) after urination. It is considered impure. `A’ishah (may Allah be pleased with her) said, “Wadi comes out after urination. The person should wash the private parts and perform ablution. It is not necessary to perform ghusl.” This is reported by Ibn Al-Mundhir.
Madhi: This is a white sticky fluid that flows from the sexual organs because of thinking about sexual intercourse or foreplay, and so on. The person is usually not aware of when exactly it is secreted. It comes from both the male and the female sexual organs, although the amount from the latter is usually more than the former. Scholars agree that it is impure. If it gets on the body, it is obligatory to wash it off. If it gets on the clothes, it suffices to sprinkle the area with water, as it is very hard to be completely protected from this impurity, especially for the young, single person.
`Ali (may Allah be pleased with him) said: “I used to excrete madhi, so I asked a man to ask the Messenger of Allah (peace and blessings be upon him) about it. I was shy to do so because of my position with respect to his daughter (`Ali was the Prophet’s son-in-law). He (peace and blessings be upon him) said, ‘Make ablution and wash your penis.’” (Reported by Al-Bukhari)
SahlIbnHunayf said, “I used to suffer from excessive amounts of madhi. I used to make lots of ghusl because of it. So, I mentioned this to the Messenger of Allah (peace and blessings be upon him) and he said, ‘It is sufficient to take a handful of water and sprinkle it over your clothes wherever the fluid appears.’” (Reported by Abu Dawud)
Mani (semen): Some scholars say that semen is impure, but apparently it is pure, for it is only recommended to wash it off if it is still wet, and to scratch it off if it is dry. `A’ishah (may Allah be pleased with her) said: “I used to scratch the semen off the Messenger of Allah’s clothes if it was dry, and wash it off if it was still wet.” (Reported by Ad-Daraqutni and Al-Bazzar). It is also related that Ibn `Abbas (may Allah be pleased with him) said: “I asked the Messenger of Allah (peace and blessings be upon him) about semen on clothes. He said, ‘It is the same as mucus and spittle. It is sufficient to rub the area with a rag or cloth.’