Can we just say that if between 2 points in some given circuit, there's no load, then the potential at those 2 points are same?
It depends on what you mean by “no load”.
Normally when we say “no load”, we’re saying there is nothing in the circuit drawing current. For example if nothing is connected across the terminals of a battery we say there is “no load” connected to the battery. Obviously in this case there’s a potential difference (voltage) between the battery terminals. It’s called the no load voltage.
You however are probably thinking no load means zero impedance, such as a perfect conductor (ideal wire), in which current flows but there’s no potential difference (voltage) between any two points in the conductor. That’s the assumption we make in analyzing a circuit where assume for convenience that all the “wires” between circuit components are perfect conductors.
In reality, except for supercooled conductors, all conductors have some impedance and there will be potential differences between points in the conductor. We just assume those differences are so small compared to the potential differences across circuit elements that they can be ignored.
Hope this helps.
It is better to think of this in terms of the p.d across those two points. I'll assume you are talking about ideal wires. Potential difference(voltage) is the work done moving a charge between two points. If the wires are ideal, they have no resistance, so no work is done when charges move between places on a wire. However if there is load between, then there is some resistance, so there is work done by the charges to move across the load.