First understand that there are single speed differentials and two speed differentials, the latter better known as Swiftamatics.
Take a look at page 10 of this document,
Page 10 shows the single speed differential.
Page 13 of that document shows the two speed differetial or Swiftamatic.
All differential worm gears, the big bronze part, are driven by steel worms, aka lead worms.
The different speeds between an L, LI, or LS were achieved by different cuts of the gears, same parts in the C, CI, and CS. You cannot convert a single speed differential to a two speed differential, but you can convert an L tractor to an L8 tractor by swapping out the single speed differential, changing the right axel housing to the special Swiftamatic, and maybe the left axel housing, plus adding the shifting linkage. There were bearing changes in that area and that may require changing both axel housings.
The Swiftamatic introduced a two speed axel or differential, and they were cut with 8 lead, 6 lead, and a very few rare 4 lead gear sets. There were several changes in the Swiftamatic itself, from a five cog shifter to a three cog shifter, the latter is stronger. And the internals were changed for the better in mid-1971, parts inside no longer wore away the inside of the bronze worm gear.
The 5000 series tractor uses a different breed of Swiftamatic, it looks the same but will not fit into a 500 series tractor or earlier tractor, and the center thrust pin no longer exists in a 5000.
If you collect a bunch of Swiftamatic parts, always look at the condition of the outside of the bronze worm gear first. When the teeth wear away, you have a nice slug of bronze scrap metal, and nothing else.
If you find a nice pre mid-1971 Swiftamatic with the internals trashed, the bronze gear can be machined out to fit the new style spider assemblies, but you still need good usable parts to rebuild with.
The problem with the pre ‘71’s is that parts of the spider pin actually rode on the inside of the bronze gear. As the inside of the gear wore away, steel on bronze, the spacing of the gears on the spider pin changed to a point where gears never designed to play together collide and that is a bad thing.
As a side note, all the Gravely powered L8's and C8's have oil pick-up screens right below the big bronze worm gear. 'Do change your oil filter often', the bronze tid-bits clog a filter.
Can you change just a simple L to and LS, yes if you can find the right worm and worm gear; and it is a complete teardown of a tractor to change the lead worm.