If you're interested in booking a GUIDED TOUR of the Uffizi Gallery, the cost of the tour already includes a ticket, regardless of whether you qualify for full, reduced or free ticket. You end up paying equally for the tour itself, ticket included.
If you're looking at tickets, note that it doesn't include a tour of the museum -- the museum does NOT offer tours directly, only an audio guide that you rent on the spot after you've passed security before you go upstairs to enter the museum.