Does performing the purification ritual for a major ritual (like Ghusl for sexual impurity) suffice for a minor ritual (like Wudu) or vice versa?

Primary text

The purification ritual for major impurity does not suffice for the purification required for a minor ritual, nor does the intention for one count for the other. This is because they are two distinct causes requiring distinct rulings. The evidence is the Prophet's saying: 'Actions are but by intentions, and every person shall have but that which he intended.' Since the individual did not intend purification from the minor impurity, it is not fulfilled. Moreover, they are two different causes, so the intention for one does not suffice for the other, akin to Hajj and Umrah. Likewise, since they are two forms of purity, one cannot be fulfilled by the intention of the other, unlike the comparison made to water purification where the underlying ruling (minor impurity) is the same for both Wudu and Ghusl.