I'm looking for layman-accessible nouns (or concise descriptions) for the union and intersection of sets of appointments, in the context of planning software. In this scenario appointments between an employee and a customer may be scheduled. Typically one retrieves appointments either by employee or customer, but a new search method has been requested where one can search for both an employee and a customer.
This search can either return a union of the employee and customer appointments (meaning all appointments where either of the two attend) or an intersection of the appointments (meaning only those appointments where the employee and customer both attend). Consider for example a set of three appointments:
Appointment A1 attended by Employee 1 and Customer 1 Appointment A2 attended by Employee 1 and Customer 2 Appointment A3 attended by Employee 2 and Customer 2
In case of a union of the appointments for Employee 1 and Customer 2 all three A1, A2 and A3 would be shown, whereas the intersection of Employee 1 and Customer 2 only returns A2. The nouns I'm looking for would be used to allow the user to specify which kind of search is desired and to indicate which search type is being displayed.
We've discussed a number of options with our key users, such as 'joint' appointments for the intersection, variations on 'all' and 'both' for the union and the typical 'and' / 'or' terminology, but so far all of these still proved confusing, in my opinion because they don't reflect the correct meaning exactly. The union/intersection pair does reflect this meaning, but is unsatisfactory because it's perceived as too mathematical by most users.
(I apologize if this may seem to be more of a user experience question, but I am genuinely curious how the specified meaning could be captured correctly in concise and natural English)