The "*" indicates a "sub-increment", a design or production variation not deemed deserving of an advance in "Mark".
Thus the "proper" Mk 111 rifle should have all the "fruit", the "111*" was essentially a wartime expedient. By the time the Second Great Unpleasantness erupted, the perceived need for volley sights and magazine cut-off had diminished somewhat.
One of the things that makes these rifles "interesting" is the oddball minor variations; bayonet bosses solid or "lightened from the rear, blank, semi-finished or fully-finished piling swivel "bumps" on the nose-cap, blank, semi or fully-finished cut-outs for the cat-off, various types of cocking pieces, strikers and cocking pieces, ditto trigger-guards.
Unless you get one out of a sealed factory crate, it will be the exigencies of service life and the availability or otherwise of armourers and eagle-eyed Quartermasters that will determine the "update" status of your rifle.
Consider a Lithgow SMLE sent to WW1, recovered from the battlefield, rebuilt "somewhere in
England", re-issued to a Brit, "transferred" to an
Australian unit near the front, shipped home to Oz and then getting an FTR to see service in the Pacific in the next one and finally being rebuilt again and, liberally sprinkled with all manner of interesting stamps, put into war-stores in the late '40s. Is such a rifle LESS authentic than a pristine, just out of the grease 1920?
There are lots of funnies around, notably receiver bodies that were made as Mk 111, 'upgraded to "111*" and then "restored" to "111" by the simple expedient of striking out the "*" as part of the "re-fruiting" and restoration process.
Note that the ammo changed radically with the transition from Mk6 to Mk7 ball. The sights, magazine and entire bedding regime had to change to accommodate this, just before WW1 kicked off. But they had to keep the long chamber throat because there were still BILLIONS of Mk6 rounds in the "Empire"; much of which ammo was sent ashore to some place called Gallipoli.