These theorems are usually used to find the current through (or voltage across) "LOAD" resistor, obviously Load Resistor is one through which you wish to find current (or across which you wish to find voltage drop). Obviously, Choice is yours!!! Ultimately you will have Thevenin's and Norton's equivalent circuits which are nothing but either a voltage source or current source with their internal resistance, connected across the load resistor.
With Ref. To question fig. you posted, anyone of 3 resistors can be considered as load resistors while obtaining equivalent Thevenin's or Norton's network, you have to decide through which resistor you want to find current.
I can also find Thevenin's and Norton's equivalent circuits across other two resistors and I will still be right. The original question which you have to tackle is not "Difference between load resistance and Thevenin's resistance" but "Which shall be my load resistor?" and the answer to that lies in "your requirement." Suppose if you were told to find current through resistor connected to +ve terminal of either battery and node A, you'd have selected that resistor itself as load resistor.
Actually the reason of calling that resistance as load resistance is the Thevenin's and Norton's equivalent circuits. As I said earlier, these are the simplified forms of complex network; containing either single voltage source or single current source (with internal resistance) supplying the load resistor. So the word "Load" has originated from these equivalent networks and not from non-reduced ones and thus you don't have to worry about predicting "Load Resistor" in non-reduced network, you just have to know which current or voltage you want to find.