Also, in a propellor-driven airplane, fuel consumption varies with power produced, whereas on a jet fuel consumption is basically proportional to thrust produced. And yes, on a jet the thrust levers essentially control thrust directly, whilst on a prop the power levers control, er, power. It thus makes more sense to think in terms of power when referring to props and thrust when referring to jets.
Both jets and props however produce both thrust and power, and in both jets and props best angle of climb will be the speed at which excess thrust is highest, while best rate will be the speed at which excess power is greatest.
The nature of the curves on the graphs (thrust remaining more or less equal over all airspeeds for jets and tapering off for props, and power increasing with speed for jets and remaining more or less steady for props) is due to the differing characteristics of the two types of powerplants as pointed out by Chu and KW. It simply means that Vx and Vy for props and jets will be at different points on the drag curve, higher up for jets, lower speed for props.