Keep in mind that there is an M91, then there is a 91/30. The M91 is the older version. Has a simple front sight blade and a hexagon shaped receiver. The 91/30 was the modernized version. It has a protected front sight with a post. Most have round receivers (although some used refurbed or left over M91 receivers).
The next variation was the M1938 carbine. This is pretty much a 91/30 shortened with a 20" barrel. The rear sight was shortened to an adjustment of around 1000 meters (half of the 91/30's). It's a rear area gun (similar in actual issue to the way the US M1 carbine was used). No bayonett was issued with the M38 carbine as it was not a "front line" weapon. Later, the Mosin carbines were manufactured with a folding bayonet added to the side and this was the M44. This was a front line weapon, replacing the long 91/30 in issue to troops (much like the M4 is replacing the M16A2 in today's US Army.
Finally, the last Russian Mosin-Nagant was the M91/59. This 20" carbine was made from refurbished 91/30 rifles. It 1959, they (Nobody really knows if the Russians made these, or if they were made by a satellite nation like Bulgaria) cut down the barrels, cut down the wood and made a carbine that looks very similar to the 1938. The easiest way to tell this carbine is it has a long rear sight of the 91/30, but the range markings from 1000 to 2000m are milled off.