What is the difference between madhi, wadi and mani?

Madhi: the fluid of arousal

Madhi is a thin, clear, sticky fluid that comes out when you're aroused, for example by thoughts, kissing or foreplay, without reaching climax. Often you don't feel it come out. Both men and women can have it. Ali ibn Abi Talib said he had a lot of madhi, and he asked about it through a friend because he felt shy. The Prophet ﷺ said to wash the private part and make wudu (Sahih al-Bukhari 269).

So madhi is impure and breaks wudu, but it doesn't require ghusl. Wash it off your body. For clothes, some scholars (mainly Hanbalis) say sprinkling water over the spot is enough, while others say wash it.

Wadi: the drop after urinating

Wadi is a thick, white, cloudy fluid that may come out just after urinating or after lifting something heavy. It's treated exactly like urine: it's impure, you clean it with istinja, and it breaks wudu. No ghusl is needed.

Mani: the fluid of climax

For men, mani is thick and comes out in spurts with strong pleasure, usually followed by tiredness, and it smells a bit like dough. For women it's usually thinner and comes with orgasm. Whenever mani comes out, whether awake or asleep, ghusl is required. The Prophet ﷺ said, "Water is due because of water" (Sahih Muslim 343), meaning ghusl is due because of the release of fluid. When Umm Sulaym asked if a woman has to bathe after a wet dream, he said yes, if she sees the fluid (Sahih al-Bukhari 282).

Is mani itself impure? The schools differ. The Shafi'is and Hanbalis say it's pure, while the Hanafis and Malikis say it's impure. Aisha reported both scraping it from the Prophet's ﷺ clothes and washing it off. Washing the spot satisfies everyone. See When is ghusl required?

Not sure which one it was?

Look at the signs: gushing, strong pleasure and tiredness point to mani. Without them, treat it as madhi or wadi: wash and make wudu. If you wake up and find wetness you can't identify, many scholars say do ghusl to be safe. See Do I need ghusl after a wet dream? Normal everyday vaginal discharge is a separate topic: most scholars say it breaks wudu but doesn't require ghusl.