Does the emission of semen during istinja' necessitate ghusl or changing clothes, even if it does not soil the clothes or body?

If semen is discharged during istinja' (washing after urinating or defecating) without desire, pleasure, or gushing, it does not necessitate ghusl (ritual bath) according to the majority of scholars, whereas the Shafi'is and those who agree with them hold that it does. However, if it is discharged with desire, ghusl is obligatory without dispute. As for wadi (a thick, whitish discharge) which often exits after urination and without desire, it does not necessitate ghusl, but it is impure and requires purification of the body and clothes from it.