The spermatorrhea or the pre-seminal fluid is a liquid that comes out after some sort of sexual pleasure leading to an erection. It comes out drop by drop. It is not pure according to all the Fuqahaa (Muslim jurists) and so it nullifies the Wudhoo’ (ritual ablution). It should be washed out of the penis. Any drop of it that touches any part of the body or the clothes should be cleaned. The evidence of this is the Hadeeth narrated by Imaam Muslim that Ali said, “I used to excrete very much Madhi (preseminal fluid). So, I asked a man to ask the Messenger of Allaah, sallallaahu ‘alayhi wa sallam 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 said: “Make ablution and wash your penis.” Sahl Ibn Haneef said, “I used to make lots of Ghusl (ritual bathing) because of it. So I mentioned this to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, and he said: ‘It is sufficient to take a handful of water and sprinkle it over your clothes wherever the fluid appears.’” Some scholars, however, believe that if the man secretes excessive amounts of pre-seminal fluid, he may simply splash some water over the garment. 

As for the sperm, it is the fluid that comes while one is dreaming (wet dreams) or during sexual intercourse. It flows out from the penis with strength. After, it has come out, the Muslim should wash himself, but the sperm itself is pure according to the more preponderant opinion of scholars. Imaam Muslim narrated that Aa’ishah said, “I used to scratch the sperm from the Messenger’s clothing if it was dry, and wash it off if it was still wet, then he would pray in those clothes.” Had the sperm been impure, scratching would not have sufficed and washing would have been obligatory. It is also related that Ibn ‘Abbaas said, “I asked the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, about sperm on clothes. He said: ‘It is the same as mucus and spittle. It is sufficient to rub the area with a rag or cloth.’”  

As for the fluid that comes out after having done the Ghusl, it does not require a new Ghusl because it is only something remaining from the first one. As for your question about parts of the Madhi in the sperm itself, we do not think that there are any, but you should ask a specialized person in this matter, taking into consideration that the legal ruling would not change in both cases.

Allaah Knows best.