Last time I took BART to SFO, I was a bit confused. I boarded a train at North Berkeley Station for "San Francisco International Airport / Milbrae". After the San Bruno Station, I saw SFO to my left, and then a bit behind me to my left. It then dawned on me that we weren't going to SFO -- at least not directly. The train went to Milbrae, stopped for a couple of minutes, and turned around. Next stop was SFO. It added about 10 minutes to the journey -- no biggie for me, as I had sufficient time to catch my flight. I was a little concerned that we might bypass SFO again, and then I'd need to backtrack from San Bruno. Thankfully, that's not how it works. If you see "San Francisco International Airport" on the signs, the train will go to SFO -- only question is whether it will first go to Milbrae.

As I read the maps and schedules, it looks like the Richmond Line (red on the maps) has the Milbrae-SFO trains; the Antioch Line (yellow) has the trains going directly to SFO after San Bruno. The trip planner at bart.gov is very helpful. I plug in my desired arrival time at SFO and work backwards from there. It can actually be faster to take a slightly later train at your station if that later train goes directly to SFO (extra time waiting for that later train can be less than the extra time going to Milbrae).

Traffic in the SF Bay Area is very unpredictable, and crashes/stalls on the Bay Bridge can ruin your air travel day. BART is a much more reliable way to arrive at SFO on time, and with minimal stress. Safe travels, my friends.