Berlin Transit System

Think of S for surface and U for underground as that is the way they usually function. The Flex I know is a type of ticket, 8 rides within 30 days with a duration of 24h per activation of each ticket.

S-Bahn is like the commuter rail & the U-Bahn is the subway.

I think of the U-Bahn as being like the subway system in NYC, and the S-Bahn as being like the Long Island Railroad. Both are underground in the city, but the S-Bahn goes above ground outside the central area and goes far out into the suburbs.

Another think=g, the S-Bahn is run by the Bahn (German Rail) and is in the same class as other regional trains. The U-Bahn are run by local metro rail companies.

German Rail passes include the S-Bahn but not the U-Bahn.

As suggested above, the S-Bahn makes fewer stops in the central part of Berlin but goes farther out. If you'll be there several days, you might consider a multi-day pass. My 7-day pass got me everywhere.

One thing I liked about the Berlin system is no turnstiles. Buy your ticket from a machine and just get on. You may encounter an inspector who checks everyone for tickets when the train is underway. Not having one equals a big fine.

You could think of the two systems as one of them going laterally, ie from west to east, ie to eastern most districts of Berlin, eg, to Karlshorst or Ahrensfelde from Charlottenburg.