As quoted in Khan Academy, "One way to remember these two coiling right-hand rules is that straight magnetic field lines are caused by circles of current, and straight lines of current cause circular magnetic fields." Have you come across any questions based on this in which we are asked to use the second scenario?
When do you think this applies? There seem to be two rules, each applying for 2 different scenarios.
While we normally think of a current as a lot of electrical charges moving along in a wire, a single charge moving in a straight line is effectively a current, so any question involving forces between moving charges, such as this one here, directly or indirectly uses the first depicted rule.
A special case of Ampere's force law is the force between two parallel current carrying wires so that is another example.
We can reshape a single single loop of a coil as a polygon with straight sections and summing up the magnetic forces of all the straight sections would give us the total magnetic force of the loop so this is how the two rules are related.
This libretext webpage represents a single coil of an electric motor as an assembly of straight wires for easier analysis of the forces and torque produced by an electric motor as depicted in the diagram borrowed from there excellent webpage below, so any questions involving electric motors directly or indirectly use the straight current rule.
straight lines of current cause circular magnetic fields. Have you come across any questions based on this in which we are asked to use the second scenario?
This is a very common and useful example: the magnetic field due to a thin straight wire carrying a current $I$. Straight current-carrying wires are very common in real life.
In this situation it is known (from the Biot-Savart law) that the magnetic field at a distance $R$ from the wire has intensity $B=\frac{μ_0I}{2πR}$. The direction of the magnetic field $B$ depends on the direction of the current $I$, and you can find it with the right-hand rule (in this scenario you can see the current as the thumb).
