The set stamps in the artwork you describe are the pre-release cards for most part. 
In the earlier sets it mentioned actual pre-release, like this pre-release Aerodactyl from the Fossil set. But later on this changed to the set symbol (and usually a separated promo card), like this pre-release Seviper for SM Burning Shadows.
The cards from the EX era which are Reverse Holos also feature their set symbol sometimes, like this ‘Reverse Holo’ Rayquaza from EX Emerald (also note the different holofoil pattern - with Pokéballs in this case - which all EX Emerald ‘Reverse Holo’ cards will have. The golden name, HP, and rarity symbol is an indication that it’s a ‘Reverse Holo’ variation of a Holofoil Rare card, as I mentioned earlier. Here is the same Rayquaza as a regular Holofoil Rare to see the differences with its ‘Reverse Holo’ version.
I believe there are also some cards with set stamps which were not pre-release cards. Not sure which and how many tbh, but I do know of this recent Garchomp from Unified Minds, which was originally released as a store-exclusive in The Netherlands and Belgium (although if I’m not mistaken was also released in the US later on).
So there are different type of cards which can have the set symbol in the artwork. Most of those are pre-releases, though.
Ah, so that’s the purpose of those letters at the bottom-left of Japanese cards. I actually had no idea they were used as indication of which cards were legal and which were out of rotation for the Pokémon TCG game in Japan. Here is a bit more information about it apparently. Thanks for asking, I’ve learned something new myself now. 
Only some of my own threads I have bookmarked in my browser, like my Base Set Pikachu article, 1st editions stamp variations article, Teach Sets article, National Index collection, etc. But overall I just know where to look for certain information on Bulbapedia and this forum. One thread which might be interesting to read through all threads is this one. It contains an (unfortunately pretty outdated 
) list of all Pokémon articles in the Articles, Guides, & Resources section. I’m not sure if @pokemontrader is still active, but if he is, here a reminder that thread could use an update. 
I personally find it very useful, although I also know loads of new articles which has been posted in the past two years, including some of my own (1st edition stamps, Teach Sets, National Index), as well as loads of others like the No Rarity guide by @shizzlemetimbers, the fire-proof saves threads of @silversnorlax204, the Base Set ©1999-2000 print run by @styluspt, and probably more I forgot about.
Anyway, I’m active for little over 4 years now, and have learned A LOT from being active on this forum. So with all the links I provided for you I just know where to look for or know where they are located. I don’t have a folder or something with all these links saved, except for the few I’ve made myself and use the most.
Greetz,
Quuador