I'd have used the terms simulationist and gamist.
Gamist xp is xp as award. Gamism means challenging the players. If the players meet the challenge, they get xp. If they exceed it, they get xp faster. If they fail, they don't get any xp.
Simulationist xp is characters in the fictional world getting better at tasks by performing them, receiving training, or thru study. Some systems grant xp for each success, in others a character learns more from failure. It doesn't matter, the point is that this is more realistic than xp as award. I'm not sure if this is quite the same as your xp as reward, but it seems pretty close.
Gary Gygax discusses this distinction on page 85 of the 1e DMG, when he defends 1e's gamist xp/xp as award -
Note: Players who balk at equating gold pieces to experience points should be gently but firmly reminded that in a game certain compromises must be made. While it is more "realistic" for clerics to study holy writings, pray, chant, practice self-discipline, etc. to gain experience, it would not make a playable game roll along. Similarly, fighters should be exercising, riding, smiting pelts, tilting at the lists, and engaging in weapons practice of various sorts to gain real expertise (experience); magic-users should be deciphering old scrolls, searching ancient tomes, experimenting alchemically, and so forth; while thieves should spend their off-hours honing their skills, "casing" various buildings, watching potential victims, and carefully planning their next "job". All very realistic but conducive to non-game boredom!