Originally the aircraft was designated as Bf 109 by Reichsluftfahrtministerium (German Aviation Ministry, RLM), since the design was submitted by the Bayerische Flugzeugwerke (literally “Bavarian Aircraft Factory”) company. However, the company was renamed Messerschmitt AG after 11 July 1938 when Erhard Milch finally allowed Willy Messerschmitt to acquire the company. Subsequently, all Messerschmitt aircraft that originated after that date, such as the Me 210, were to carry the “Me” designation. Despite regulations by the RLM, wartime documents from Messerschmitt AG, RLM and Luftwaffe loss and strength reports continued to use both designations, sometimes even on the same page.[30] All extant airframes are described as “Bf 109” on identification plates, including the final K-4 models,[31] with the noted exception of aircraft either initially built or re-fitted by Erla Flugzeugwerke, which sometimes bore the Me 109 stamping. “Me-109” is usually pronounced in German as may hundert-neun (”hundred-nine”) while English-speakers usually say “emm ee one-oh-nine”.
http://en.wikipedia.org/wiki/Messerschmitt_Bf_109
By 1971 I had a huge 1/72 scale model WWII air force of pretty much everything I could get my hands on from any country (even Italy). I was confused at the time because some model kits were called “ME109” and others were “BF109”. I was in high school and had lots of books on the subject, however, this was always a mild mystery to me. I knew where the ME came from, but not the BF.
I just used both prefixes interchangeably.