Wow, you've missed out on an unbelievable amount of stuff.
Prepare yourself for a journey of immense proportions.
- A shiny Pokémon is a Pokémon with an unusual color pattern. These Pokémon are very coveted by players but have apart from the different coloring absolutely no more value than the normally colored Pokémon of the same species. It more or less a novelty for collectors purpose.
- A Battle Frontier is a place where players can compete in certain battles with ingame trainers using specialized rules. It's more or less a tournament meets endurance/survival. It's much harder than the ingame trainers as their Pokémon are trained in such a way that they are at the peak of a Pokémon's potential (more about that later). The purpose of it is to receive Battle Points (BP) to trade in for very rare items and TMs.
Apart from these you asked for, you missed out on 4 generations of Pokémon.
1st Gen were the original Red, Blue and Yellow games, 2nd Gen are the Gold and Silver games you mention + the Suicune-themed Crystal game.
Following that came the 3rd Gen with Ruby and Sapphire, latter also remakes of the Red and Blue games, Fire Red and Leaf Green.
Later also came Pokémon Emerald, the Yellow/Sapphire of 3rd gen.
These games introduced, apart from new Pokémon (like ever gen really), new battle mechanics such as Abilities, Natures and the true introduction to Effort Values (EVs) and Individual Values (IVs) which are basically the 2 things that determine how strong a Pokémon will eventually be.
Along with Gen 2 came the Held Item system which has now become even more important and engaging, making held items sometimes of game-changing importance.
Another aspect is Double Battles which is basically a 2 vs 2 instead of the normal 1 vs 1.
This gameplay is immensely fun and demands a lot more strategy of the players.
Gen 4 brought with it a lot more changes as well, the introduction of online Wifi battles being the most popular.
People can now play against other players through WiFi or trade online from the 4 corners of the world.
Another change is the separation of moves in categories of Special moves (moves that don't make physical contact between Pokémon) and Physical moves (the opposite).
Gen 4 games are: Diamond/Pearl/Platinum and the remakes of Gold and Silver, Heart Gold and Soul Silver.
Gen 5 brought even more gameplay additions.
Among them is the evolution of Double battle in the form of Triple Battle.
Basically, 3 vs 3.
Also comes Rotation battle: 3 vs 3 where you fight 1 vs 1 but can rotate your pokémon around instead of switching out.
The best change to the game imo is the fact TM's now no longer are 1 time use. You can teach Pokémon a TM move as many times as you want.
Now every pokémon you have can learn Earthquake or Thunderbolt.
Gen 5 games are Black and White and later, for the first time, came the direct sequels to these games in the form of Black 2 and White 2.
The current gen, Gen 6, only has 2 games so far but a 3rd game is almost guarantied.
X and Y are the first Pokémon games with 3D environments and Pokémon (on handheld consoles at least) and looks stunning to say the least.
This gen now introduces a new type as well, something not seen since gen 2: Fairy type.
I'll refrain from giving out more info as not to spoil your eventual future gameplay fun, but the last thing I'll say is that you definitely will want to play a game from each gen before starting the next gen.
Each game has fantastic story and a huge amount of new Pokémon each gen.
You can easily pick up each game without too much trouble as the central gameplay hasn't changed at all.
Have fun :)