The Me-209 was actually used for two seperate projects.
The first one was racing plane. It was a completly different aircraft from the Bf-109 and was designated that by Messerschmitt for propaganda purposes. So atleast is what I have read.
It had the same engine as the Bf-109 the DB-601 but was designed slightly differently. The cockpit was farther back and it had a wider undercarriage. On April 26, 1939 Luftwaffe test pilot Fritz Wendel broke the world speed record wwith it by obtaining 756 km/h (470 mph).
The aircraft however was little more than a racer. All the engine coolant systems and the wings prevented it from carrying armament. Handling was also not very good. Messerchmitt did attempt to make a fighter varient out of it by lengthening the wings and modified tail to improve the handling and added 2 MGs to the nose. All of these modifications however destroyed the speed of the aircraft to the point that it was less than the Bf-109E.
The speed record of the Me-209 however was not broken until 1969 by a modified Bearcat.
The first picture below is of the Me-209 racer.
Specifications (Me 209 V1)
General characteristics
Crew: one, pilot
Length: 7.24 m (23 ft 9 in)
Wingspan: 7.80 m (25 ft 7 in)
Powerplant: 1× Daimler-Benz DB 601ARJ , 1,342 kW (1,800 hp)
Performance
Maximum speed: 755 km/h (470 mph)
The other Me-209 project was a modified version of the Bf-109 basically. The design basically took a Bf-109G airframe and was to imcorporate a DB-603 engine but instead used a Jumo-213 due to lack of DB-603s.
Modifications included a new tail, wider undercarriage, and an annular radiator which gave the engine a superficial resemblance to a radial powerplant. When the Me-209V-5 first flew in 1944 it was 50kmh slower than the Fw-190D and therefore was cancelled.
Specifications (Me 209 V5)
General characteristics
Crew: one, pilot
Length: 9.74 m (31 ft 11 in)
Wingspan: 10.95 m (35 ft 11 in)
Height: 4.00 m (13 ft 1 in)
Wing area: 17.2 m² (185 ft²)
Empty weight: 3,339 kg (7,346 lb)
Loaded weight: 4,085 kg (8,987 lb)
Powerplant: 1× Db 603G , 1,397 kW (1,900 hp)
Performance
Maximum speed: 678 km/h (423 mph)
Service ceiling: 11,000 m (36,080 ft)
Wing loading: 238 kg/m² (49 lb/ft²)
Power/mass: 0.36 kW/kg (0.22 hp/lb)
Armament
1 x 30 mm MK 108 cannon
2 x 13 mm MG 131 machine guns
Below the Me-209 racer picture is a Me-209 fighter picture.