The airport is in Renfe Zone 2, whereas its in AMB Zone 1, the latter of which always takes priority. So if you were to buy a T-10 at the station, a 1 zone ticket would be perfectly valid. If you were to to buy a single from the airport to Sants, that's a 2 zone ticket.
Just to add to previous posts: a T-10, just like other multi journey tickets, is valid for up to 1h 15m per journey in zone 1 with unlimited changes between transport types. You cannot, for example, get off at the Sagrada Familia, take a few photos and renter the metro hoping to use the same journey. This is detected by the system and a new journey is started. T-10s can be used my multiple people at once, it is just a case of validating the ticket for each person who is travelling.
There is a good tool called T-Estalvia, available online, which calculates the cheapest ticket combination based on the number of days, number of passengers, age of passengers and number of zones being crossed.
Yes, many sights in Barcelona can be reached on foot, but it does all add up. One end of the Rambla to another, for example, is a good 20 minutes walk. Same goes from the bottom of the Rambla to la Barceloneta. So the metro is very handy, and at only 98 cents per journey if using a T-10, it's a steal compared to London.