Each class has it's own colour, but the only reason we have them is because they all have their own features, as well as their own limits.
The Trainer is someone who focuses entirely on challenging the gym leaders around Elix, and the Elite four. Their main goal is to defeat the Pokemon Champion. They could eventually become gym leaders, after they defeat the Elite Four, and the champion. They aren't allowed to join contests, breed, or work for a professor- and are moderately less likely to find any rare items.
The Coordinator focuses entirely on winning contests, be it beauty, cool, tough, smart, cute, etc. Their main goal is generally to either win first place in all the contests they participate, or simply have the most attractive, intimidating, cool party, etc. They cannot fight gyms, breed, or work for a Professor- and are moderately less likely to find rare items.
The Breeder is someone who simply makes eggs and hatches them- selling them to others depending on the breed. They focus on collecting Pokemon, specifically, and selling the offspring. They also generally are known to keep Pokemon that are prone to evolving according to happiness- such as Pichu, or Riolu. They aren't allowed to join contests, fight gyms, or work for a professor- and are moderately less likely to find rare items.
The Researcher is basically a Professor's assistant. They're given tasks and assignments to complete by an NPC, and will get rewards and the such for completing them. They're a bit more likely to find rare Pokemon, and if they've done a good enough job completing their tasks over a certain period of time, they could also become a Professor. They aren't allowed to join contests, or breed- and are slightly more likely to find rare items.
The Collector is primarily someone who searches for rare items. They collect them, keeping them for themselves, or sell them to the highest bidder. These items are generally evolutionary stones and the such. They aren't allowed to join contests, breed, or work for a professor- and they are moderately more likely to find rare items and Pokemon. Their chances of finding shiny Pokemon are multiplied by three.