The intuition of the use of a SORT as an ALTERNATIVE within a type definition group (or at some other place together with a freeness requirement) is that all values of SORT are taken as generating elements in the free construction. Technically, they are injected into the new sort by a subsort injection function. If there are two SORTs used as ALTERNATIVEs having a common subsort, the latter is copied only once due to the commutativity requirements between the injection functions (cf. the set J of axioms used when reducing subsorted specifications to many-sorted specifications in [CMKB+96]).
Acknowledgements
Thanks to Maura Cerioli, Bernd-Krieg-Brückner, Anne Haxthausen and Peter Mosses for various discussions and to Maura for essentially contributing to section 1.