Yes they are different. Actually there are four different Gameboy products on the market.
First is the oldest, the original Gameboy Advance. It was a color screen with no backlight.
Next came the Gameboy Advance SP. This is a more compact version of the original, it can fold in half, but it also has a backlit screen that allows you play it in the dark. Nintendo recently came out with a brighter version of the product that gets rid of the backlight and adds the light behind the screen, making the colors on the screen more vivid.
Then you have the Game Boy DS. This is a larger system than the SP, and more powerful too. It also includes two screens. The top screen that acts as the monitor, and the bottom screen that acts similar to a pda. It comes with a stylus and you are able to interact with the game on it.
The newest product is the Game Boy Micro. It is nice in that it is very compact, so you can take it anyway. The biggest drawback, especially for Pokemon enthusiasts, is that currently there is no way to link up with another GBA, using a cable link or otherwise. Quite limiting, if you ask me.
Now for the games themselves. You appear to be at least familiar with the Red/Green/Blue/Yellow versions that came out years ago, so I will not cover that.
The next versions were Gold/Silver/Crystal. These games took place in the Johto region, which is just west of Kanto. Like its predecessor, you start out as a boy who looks like Ash from the cartoon. This time you visit Professor Elm (another tree), and you get to choose a starter from Chikorita, Cyndaquil, and Totodile. They are Grass, Fire, and Water, respectively. Same as RBY. The concept is the same as well, with a few new twists. First, your Rival is not Gary. It is a red-headed punk that no matter how many times you whip his candyass, still thinks he is better than you. You now set a clock at the beginning, which controls the night and day aspect of the game. This was a great addition that sadly hasn't been used since. The other great thing is that some Pokes only could be caught in the morning, afternoon, or evening. Again, sadly that was abandoned as well. The pack was also expanded with 4 pouches, allowing you to divide up your items, TM/HMs, Poke Balls, and important items (bike, keys, etc.). They also added a new module called PokeGear. This is where you could view your map, listen to the radio, and register phone numbers for trainers/characters to call you. Some trainers would ask for rematches while some trainers would tell you about swarms of rare Pokemon. Pokemon were also given the ability to hold one item. Some held items even gave the Pokemon a certain advantage. The game included 100 new Pokemon and two new types - Steel and Dark. It also include new evolutions - Blissey/Steelix/Scizor/Slowking, new pre-evolutions - Pichu/Magby/Elekid/Tyrogue/Shmoochum/Iggybuff, Pokemon evolving through a trade, Pokemon evolving through trading while holding items, and even Pokemon that evolve when they are happy. Another great addition is that now most Pokemon could be male or female. This came in handy for the greatest innovation of all - Breeding. There was a Daycare center where you could drop off a male or a female of the same species and after walking a predetermined amount of steps, it would produce an egg. Then, after walking a predetermined amount of steps, the egg would hatch into a Lv5 version of the female Pokemon. Not only that, but Ditto could be used to mate with either male or female to produce eggs. After defeating the E4 in Johto, you were given a ticket to ride a cruise ship that takes you to Vermilion City in Kanto, where you start a new adventure to collect the 8 badges in Kanto, including getting a badge from Gary (called Blue), who apparently has fallen from the short-lived Kanto champ to a lowly gym leader. There is no real point to collecting badges though since you cannot fight the E4 in Kanto. Instead, Professor Oak will open up a place called Mt. Silver, where Ash (called Red) is waiting to battle you. He is surprisingly easy to defeat and then leaves without saying a word. A little anti-climatic for me. It was like they were in a rush to finish production so they never finished.
A few years later, Ruby/Sapphire was introduced. This was dubbed as an entirely new game than we have ever seen. Well, they were half right. At the start, you are able to choose between a headband wearing boy or a dewrag wearing girl. The boy is named Brendan and the girl May. You beginning moving into a town in the Hoenn region, and your Rival is whomever you didn't choose to start with. Their dad is Professor Birch (see the pattern?). The storyline has a nice twist, but you end up choosing between yet another Water/Fire/Grass starter - Mudkip, Torchic, or Treecko. The game has 202 Pokemon, but roughly half of them are re-treads from the Kanto region. As I said before, the beginning appears promising, as your dad appears to be a gym leader, but then the typical storyline unfolds - earn badges, defeat E4, gotta catch 'em all. This game does introduce natures and abilities though, which is nice. A nature is a personality that a Pokemon has (there are 24 different natures). While a few natures don't affect your Pokemon's stats, the others do. For example, an Adamant nature will increase the Pokemon's Attack by 10% and decrease its Special Attack by 10%. Abilities give different Pokemon advantages during battle, and sometimes out of battle. For instance, if a Pokemon has the Inner Focus ability, it will not flinch, even it it is attacked by a move that would make it flinch. The game also includes new moves, TM/HM, and characters that you run into during the course of the game. The Breeding ability was improved, organizing Pokemon into Egg groups and improving the Effort Value point system. It also introduced Secret Bases and mixing records. A Secret Base is a hideout (for lack of a better word) inside a tree, bush, or rock wall. Here you can decorate your base with cool (and lame) items that you purchase at point throughout the game. Mixing records is when you link up with another player. What happens is that their Secret Base will show up on your game, and you are able to go to their base and even battle them. A few new pre-evolutions were added that can only be found through breeding with the female holding a particular item. Overall, I found it lacking in originality but the playability was still nice.
The following year FireRed/LeafGreen came out, which was a remake of the original version. They incorporated the breeding, natures/ability, and hold items from the previous versions, and also added the Sevii Islands, that you could go to once you defeated Blaine on Cinnabar Island. It also put a limitation on the National Pokedex that didn't allow you to get Pokemon past the original 150 Pokemon until you had gathered 60 species of Pokemon and completed the quest on the first three islands. This game also introduced the ability for a wireless connection to other FRLG games. You could gather in a room with other trainers and chat or trade or battle with them. The developers also added hidden berries and items throughout the game.
Emerald is the most recent game, that is a variation of Ruby/Sapphire. There were a few improvements to the Abilities, berries, and the storyline. You can now catch all 3 Legendary Pokemon, but they will be Lv70 so there is a drawback. Emerald is also wireless compatible, so you can link up with FRLG. Everything else has pretty much already been talked about.
The next version that is due in Japan this year (summer, I think) is Diamond/Pearl. We have only seen screenshots on this, but it appears the graphics are more 3-D than flat and it also looks at though you can have a Pokemon walk with you, similar to Pikachu in Yellow.
That is about it. Hope this helps.