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The M2 was considered to be a more affordable, simplified version of the 1954 Leica M3. Notably, the frame counter of the M2 was composed of a disk plate beneath the film advance lever that had to be manually reset to zero after reloading. This system was close to that of the Leica III series, and unlike that of the M3, which is an independent frame counter, visible through a window in the top plate, that automatically resets to zero when the film take-up spool is removed.
The rangefinder system was also simplified from that of the M3 and this made it potentially more prone to rangefinder flare. The M2 has a rangefinder with a 0.72 magnification and frame lines for 35, 50 and 90mm lenses instead of the 0.91 magnification and 50, 90 and 135mm frame lines of the M3. This made it better suited for photojournalists who favor shorter lenses or for spectacle-wearers using a 50mm lens who sometimes find it difficult to see the frame lines on the M3. The ground glass frame line illumination window of the M3 was replaced with a fresnel-type plastic lens. Finally, the ornate beveling around the various windows on the front of the M3 were flattened on the body of the M2. Unlike the M3, the widest frame lines were not always visible so only one set of frame lines were ever displayed at one time. All M2s are single stroke advance.
The M2 was followed by the still simpler Leica M1 and then the Leica M4, which used a similar rangefinder design but re-introduced the M3 style frame counter and added a faster loading system and a canted rewind lever.
On the present-day used market the M2, originally intended to be more "affordable", sells at prices only slightly lower than the M3. Both cameras are made to a similar level of quality, and the M2's frame lines have proved to be more versatile over time, with all subsequent Leica rangefinder models having 35mm frame lines included.
Here's a video of photographer KingJvpes shooting on the streets of San Francisco with a Leica M2: