Typically the difference exists for competitive reasons. The fare to / from FRA is competing with other carriers for those routes. The through fare is likely not as competitive.

There is a potential flaw to purchasing two separate tickets, you are gambling on the "on time" performance for that day. With separate tickets, if the first flight is delayed and you miss the second flight - tough luck. You may have to pay the change fee for the second flight, fly standby, etc. The airline has no obligation to accommodate you for simply missing the originating flight of a ticket. If it is a single ticket, the airline will then be responsible for the missed connection.