I'm currently looking for reference games for these two sub-genres.
1 - Metroidvanias (ala Super Metroid and Castlevania: Symphony of the Night)
The essence of these titles is a closed environment in which you uncover objects that open up various areas.
Thus, you need to reach certain areas to upgrade your avatar in one way or another in order to gain access to other areas.
I'm already familiar with the Castlevania sequels using this model on the Nintendo DS.
2 - Adventure (such as Zelda: A Link to the Past)
The essence of this title is a top-down game where the avatar gathers items which enhance their capabilities. The world, once again, is rather open-ended, but the dungeons and some worldmap features clearly ask for specific avatar items that the player must find in order to proceed.
Thus, either side-scroller or topdown game where the avatar's advancement is marked by items or powers earned from achievement undertakings (as opposed to acquiring experience points).