Kwaad is basically right. Traditionally, RPG games are ones that focus on character development and that's about the limit of the definition. These days most games borrow various RPG elements to add more gameplay depth, hell even Madden has a gameplay mode with individual stat tracking that changes over time through training.
On the PC side and with traditional D&D the role to be played is determined by the player. The story exists solely to give them a setting for that character to explore. Western RPGs continue that practice Oblivion being a perfect example. These games tend to sacrifice specific storytelling for a wider range of interactivity.
Console gamers are far more used to Japanese RPGs. These take the opposite approach to western RPGS. The role and story arc are entirely predetermined and the gameplay is focused on tactical decisions. These game sacrifice player choice to tell a specific story.
Both can be quite entertaining although they tend to appeal to different audiences.
