How can it be that one who intentionally has a wet dream during the daytime in Ramadan is only required to make up that day, while one who intentionally breaks their fast is required to make up the day and offer expiation, and even continuous fasting would not compensate for it? And is it permissible to merely bathe after a wet dream?

A wet dream (nocturnal emission) with the discharge of semen during sleep does not invalidate the fast. However, intentionally discharging semen during the daytime in Ramadan (definition) invalidates the fast and necessitates a make-up fast (qada'). Some scholars also require the major expiation (kaffarah (definition) kubra). Whoever intentionally breaks their fast in Ramadan through sexual intercourse must make up the fast and offer expiation. If it is by other means than intercourse, the majority of scholars hold that only a make-up fast is required. Some scholars, however, are of the opinion that the major expiation is also required in addition to the make-up fast. The hadith (definition), "Whoever breaks a fast day in Ramadan without an excuse, the fasting of a lifetime will not compensate for it, even if he fasts it," is weak. If a wet dream results in the discharge of semen, ghusl (definition) (ritual bath) is obligatory; if no semen is discharged, ghusl is not obligatory.