Everyone knows this thevenin equivalent, but is it the same as this?
Yes. When you have a series circuit like the one on the right, the order of the R and the V can be changed, and the circuit will still behave exactly as before (as long as you keep the polarity of V the same with respect to A and B, and don't accidentally swap it).

This is an ideal circuit. If you had some sort of 'real world' feel that urged you to add more components or connections to it, for instance, the power supply might have one terminal grounded, or the point between the R and the V might have some stray capacitance to ground, then it would not be equivalent if the order was reversed. But then it wouldn't be that simple circuit.