Actually there is only 2 version of the 616 at any given time ...
616 Medium ( this is the official designation, medium referring to general pen size ) ; its been referred to as Big, Jumbo etc etc but Hero only eve referred to it as Medium
616 Small ( again referring to general pen size )
However the pen was released way back in the earl 60's ( specifically June 1961; sorry no price for guessing why its numbered so ) and between then and now there is some minor change due to needed re-tooling, molds but more so during the early 90's a major re-design of the pen going from a single piece ink coupler / collector to 2 piece design, that's where the slight difference in section profile between different production 616 Medium. The 616 small go through the same re-design but the section remain the same as the change is in the section inner profile.
Over time there is some variant , the 616-1 which is a 616 small with a slightly more slender cap individually boxed for export, 616-2 which is released 2012 and still around, this is the more up to date 616 small colored version with a longer cap topped with a gold plated clip and a plastic cladded jewel color matched to the jewel. 616A, released 2014 which is yet another 616 small but now in youth friendly colors.
The 616 Medium had no specific variation other than the one wit so call gold cap, the cap in earlier ones are actually TigP finished , and the later or current ones are gold plated. They are no different than normal 616 other than that they had a differently finished cap.
The 612 is a totally different pen , though having a hooded nib its not a 616 varian
The 666 is the 616 variant with the Calligraphy nib ALWAYS
The 225 /226 is the Dual use pen variant of the 616 small and medium respectively with a smaller ink sac and a shortened twist to extract Ballpoint at the barrel end
Doctor the brand is Hero's sub brand specifically targeting school / student market and the 616 Doctor is no more than re batched 616 , usually sold in individual vac sealed card package tha's suppose to hang on store shelf. There was always a myth that certain variant of 616 is better than others but over time and a large amount of samples this had never proven right. There is indeed a variation of quality mostly due to batch variation as well as where the pen is produced.
And finally of course there is variant of 616 vintage ones that were produced in old days that exhibit specific cue that's not around now , say double jewel , or those elusive vintage colors. And then of course Hero pretty much license ( or in those days its likely called cooperative sharing ) the 616 pattern to almost all 2nd / 3rd tier local / independent pen manufacturers and many had their own 616 variant and many are equally or even more interesting than the original. Some are even totally re-styled and one would not recognize its a 616 variant as only the innards remain.