When I learned this stuff everyone used "conventional current" as specified by Ben Franklin et al, where current flows from the battery positive terminal through the various components entering at the positive side and exiting on the negative side, then back into the negative terminal of the battery.
Today many (most?) people are taught to think in terms of electron current, which exits from the battery negative terminal and re-enters at the positive terminal. The way you frame your question says this is the convention you're using.
Regardless, potential difference across a load like your resistor will be positive if measured one way across the resistor, and negative if measured the other way. It's entirely a matter of which resistor terminal you define as your zero point.
Editorial remark: I think it was a very very bad idea to switch to teaching electron current instead of conventional current. Now every conversation has to begin by defining terms, and I fail to see that anything was gained in return.
Think of the current source as a very high voltage with a very high internal resistance. Thus the changes in load resistance are masked out by the internal resistance. The plus end is still plus, the minus end minus, no different to a battery.
Better to think the current source pushes a current through a load resistor, not across one. There is therefore a corresponding voltage across the load resistor. As the current does not change with the load resistor, the voltage changes to maintain the current. With a very high load resistance, the voltage across it is high. Thus current sources may have a voltage limit called compliance, or connect a supplementary resistor across them that limits the voltage to some reasonable value even if there is no load. This might be called the burden in some situations.
The terminal that the current enters is more positive than the other.
The word "difference" tells you that it must be positive because you cannot have a negative difference.
When a current source pushes a current across a resistor in through the negative end and out of the positive end, is potential difference across that resistor positive or negative?
