The GTS originated in gen 4, mostly because The Game Boy advance games didn't connect to wifi. :P
Pokemon Bank was made in generation 6, but can transfer from 5 to 6/7, from VC GB (RBY/GSC) to Gen 7, and from 6 to 7.
Yes, people had to trade from game to game; however, some games couldn't trade (For example, Japanese Red with English Red, because both games would crash and lose all data due to other regions characters not existing in the opposing game's data).
While these have not been around forever, there was a GBA Game similar to Pokemon Bank, Called Pokemon Box, for the Gamecube (For Gen 3). It allowed you to store Pokemon in extra boxes (Quite literally, a Pokemon Storage device), but didn't have between game transfer options (It can't receive RBY/GS Pokemon) like bank does. :P
Edit: GBA/GB games traded via link cables that plugged into each Gameboy (or Gameboy Advanced), making it hard to trade with people from other countries without them visiting your country or you visiting theirs. This wired communication was replaced by infrared in the DS.
Hope I helped!