How can one differentiate between a husband's semen and a wife's semen after ghusl if the husband's semen continued to be discharged for two days and both had the same smell and consistency? And does its discharge onto clothes after it has entered the vagina render them impure?

If a woman finds semen with its characteristics after waking up, she must perform ghusl, because it is her own semen. Her husband's semen found in her is only ruled as such if she had intercourse and did not reach orgasm (e.g., if she was asleep, coerced, or young). However, if she reached orgasm during intercourse, then the discharge is either her semen or a mixture, and in both cases, ghusl is obligatory. If it is merely discharge and not semen, then ghusl is not required for her, but it invalidates ablution (wudu'), and the more cautious opinion is to consider it impure.