Standard shells in most shotguns are 2-3/4"
Standard shells in a .410 are only 2-1/2"
".410 bore" is the proper nomenclature since it's defining bore diameter and not gauge. "12 gauge" is the proper name for a 12 gauge since it is using the equal lead ball method of definition. A 12 gauge could also be called a ".729 bore". The old British method of calling what we know as a 12 gauge a "12 bore" was incorrect nomenclature.
Also people who say .410 bore is 36 gauge are only repeating a flawed marketing thing Remington did many years ago that was actually wrong. .410 bore is closer to 67 gauge or somewhere around there.
In the world of 12 and 20 gauge (and 16?):
"Magnum" shells are 3" in length
"Super Magnum" shells are 3-1/2" in length
I've never heard of "magnum" 2-3/4" shells and it would be a huge misnomer since every manufacturer I know of defines "magnum" as being 3" shells for 12 and 20 gauge. It does NOT denote a more powerful loading but only a longer shell length. Most 3" shells are more powerful than 2-3/4" shells but it isn't required for them to be called "magnum" shells. Only the length is required for that title.
The reason your manual mentions .410 bore is probably because it's a universal manual for all guages/bores of the same model. If your shotgun isn't a .410 bore then you ignore the mention of it. It is only put in specifically because it is different from all other gauges of shotshells in terms of standard length.
The rifling on shotgun slugs adds a bit of a spiral to the flight path and not a true spin. It works to even out inconsistencies in the balance of the slug so instead of hitting 4' off in a random direction it will spiral within the same 1' area. It serves a double purpose of also working as a crush zone for when firing the slug through tighter chokes. The ribs on the sides that act sort of like rifling also crush far more easily than the main body of the slug if it's forced through a choke tighter than it is in diameter. Some people also mention how it reduces barrel contact so reduces friction but I don't know about that either way so can't really comment.