Often referred to as milestones, these in-game achievements are like regular achievements except that they only count in the context of the game. Unlike Trophies or Achievements, they are not cross games.
They are usually called milestones or challenges in the context of the game. They reward you with different things. some give you extra experience for completing them (example: Need for Speed: Hot Pursuit has milestones such as drive 1000 miles which rewards you with extra bounty). Others have in-game achievements that end up unlocking real Achievements or Trophies (Splinter Cell: Conviction and Uncharted 2).
In-game achievements are the most present on Wii games. They also used to exist on the PS3 and were PS3 exclusive to fill the gap between the 360 version before Trophies were invented.