Not exactly.
In the early 1930ish both Messerschmitt and the Bayerische Flugzeugwerke where forced into a joint venture by the goverment since both where in a financially delicate situation.
That is, the Messerschmitt factory was now under the roof of the BF factory with Willy Messerschmitt being the chief constructor.
All designs developed under BF had the initials Bf, obviously, that is the Bf108, 109 and 110.
In 1938 BF turned into Messerschmitt A.G.
All new developements from now on recieved the initials Me: Me 210, Me 410, Me 262 and so forth, while the older designs retained their original Bf designations.
To make the confusion complete, all planes build prior to the birth of Messerschmitt A.G. in 1938 are Bayerische Flugzeugwerke products:
Bayerische Flugzeugwerke Bf109 for instance.
The same plane produced in 1938 or later would be a Messerschmitt Bf 109.
