Using pot as variable resistor: should wiper be connected to spare end terminal?
Electrically, these 2 circuits are equivalent.  However, the advantage of the circuit on the right is that if the internal moving tap loses contact with the resistive element, the circuit still appears as a resistance rather than an open circuit.  The latter can cause problems with some applications (for example, causing a voltage regulator to lose regulation or generate a large voltage). That is why most designers use the circuit on the right.