First off the BF109 was designed in the mid 30s. Second the MG17 and MG42 were both adaptations of an older design known as the MG30. The MG30 was the pattern for all German MGs during the war. The MG15 and later MG17 were adapted to use in aircraft, the MG34 and MG42 were adapted for use on the front lines.

Aircraft need special designs because of the unique environment in which they were used, having to function in extreme cold not normally seen at ground level, and during the turns which would put massive g forces on them. They also had to be synced to fire through the propellor and fired remotely from the cockpit.

Even the Americans had different variations of the M2 .50 cal MG which they used in aircraft.

A key difference between the MG 17 and the MG 34/42 was that it fired from a closed instead of an open bolt, allowing it to be synchronised to fire through a propeller (the Bf 109 and Fw 190 both carried a pair of cowling mounted MG 17s until around 1943). It was also cocked by a compressed air mechanism, the mountings not being accessible in flight. As /u/roosterrugburn says, many German designs were closely related, the MG 30 forming the basis for the Luftwaffe's MG 15 (flexible) and MG 17 (fixed) guns as well as the MG 34; in turn the MG 34 was modified for aerial use as the MG 81, increasing its rate of fire to around 1,500 rounds per minute (rate of fire being crucial in air combat where engagement windows could be very brief).

George M. Chinn's The Machine Gun has a section on aircraft weapons, including the Rheinmetall-Borsig and Mauser families.