What is the difference between mani, madhiy, and wadiy? Are these secretions considered impure like urine? And what is the ruling on praying in clothes that have been affected by them?

Semen (mani) and pre-seminal fluid (madhy) differ in the rulings associated with their emission. As for wadhy, it is a thick, white fluid that exits after urination due to illness, cold, carrying a heavy load, or exercise. Its ruling is the same as that of urine because it exits from the same opening.