Should have started this thread long ago...
Bulbapedia states that Apollo and Athena are "two of the four Team Rocket Executives introduced in Pokémon HeartGold and SoulSilver" and that they were merely "based" on the original Executives from GSC.
But I think that it's not true. They are, in fact the same characters. Just think about them. They have exactly same roles. Same Pokemon. Same spoken text. Same everything. The only difference is the design (the biggest thing about them is recolor and Athena's hair, note that the uniforms are practically the same as in GSC, just recolored) and the names. But back in GSC all Executives were simply unnamed. So, I'd rather say that TR Executives's names were simply revealed in HGSS.
They got stronger redesigns compared to other characters, simply because they were nothing more than nameless character-less Trainers back in GSC.
Considering the exactly same roles, same Pokemon, very similar designs, it's pretty much beyond any doubt to me that they're simply enhanced Generation IV versions of GSC Executives (Athena = Female one, Apollo = The one with Houndour) with revealed names and more character and shall be treated as same characters.
I'm refraining (and I ask you to do it too) from any Kris/Kotone analogies here. Aside from being a player's avatar, the Player Characters have no identity. Also, Kris's and Kotone's roles are arguably different considering the fact that Kris never appeared as an NPC. So, the situation between Kris/Kotone and TR Executives is very different as the Executives, being NPCs, have obvious roles and identities.
Then, there are Lance and Lambda.
The thing is... that they ALSO aren't new characters at all (though it's more debatable).
They all tree appeared in Radio Tower, remember? In GSC there were also THREE Male Rocket Executive Trainers, all appearing in Radio Tower. There's no way that they could be same character, as they would have to be bilocal. Not to mention that they use completely different Pokemon. It's obvious that there were three different male Executives back in GSC. There was just one problem about them. They had no names and same sprite. So most fans didn't even pay attention to that. Again, Lambda and Lance have same role (and more notably, same teams) as those Executives back in GSC. The only change is that Lance appeared in Slowpoke Well. Originally, that was just a Grunt.
So, in other words, NONE of four Rocket Executives is a completely new character to HGSS. The change is, that Lance and Lambda got brand-new unique designs and bigger role. As for Apollo, he's directly adapted from the final Executive who used a Houndour. Athena is a direct adaptation of the Female Executive, who was only one (appearing twice). However, having appeared in the games in the same circumstances, they aren't "Inter-Media Counterparts" or anything like that. They're same people.
This is one of those epic and awesome things about HGSS, as it unveils one of GSC's secrets, which most people didn't even notice.
Having four Executives wasn't a retcon, it was actually an EXPLANATION. So, every time you think about HGSS Executives, they weren't "created", they were "EXPLAINED". Even though Lance and Lambda's designs were created for scratch, they are still the same old Executives from GSC.
Interesting, isn't it?