You can buy either a single day ticket or airport-city day ticket. Either of these tickets let you travel in the whole Munich suburban area, which covers all of the Munich S-Bahn and U-Bahn including the airport. With a single day ticket, make sure to pick an entire network (Gesamtnetz) ticket, not a ticket that's only valid for a more restricted area.
The whole-network single day ticket and the airport-city day ticket have the same price and the same conditions.
It can be used within the selected area of validity for as many trips as you like on one day.
the Airport-City-Day-Ticket offers the same services as an MVV Day Ticket for the entire network, and at the same price, so it can be replaced by the latter if you wish.
I haven't heard of any ticket that wouldn't be valid for a round trip, except of course a single-trip ticket. It wouldn't be practical to enforce anyway since there's no indication on the day ticket of what trips you've already made with it. (IIRC the ticket does indicate where you bought it, but the rules don't say that it matters.)
There is one practical difference between the single day ticket and the airport-city day ticket. The airport-city day ticket comes pre-validated from the machine, so it can only be used on that day. The single day ticket is not validated, so you can buy it in advance, but you must validate it before traveling by inserting it into a stamping machine.
Note that if there's more than one of you traveling, there are group tickets that are cheaper than buying separate tickets (unless you're one adult and one child).