What is the difference between a Hall effect sensor and an inductive one?
First they physically work differently. In the Hall effect sensor the electrons flowing through a plate will be deflected. Thus there will be a voltage perpendicular to the current, which can be measured. The voltage will be proportional to the magnetic field strengh. So you can sense a magnet, that is near the sensor, even if it doesn't move.

For the inductive sensor you have a guiding wire, that has an AC current flowing through it. This also means, that a magnetic field ist constantly building up and collapsing again around the wire. This change of magnetic field will induce an induction voltage in a nearby wire loop (the actual sensor). The frequency of that voltage is the same as of the guidance wire and the strength depends on the distance between the wires. So you are not measuring the magnetic field strength directly, but you measure how much it is changing (mathematically you differentiate).

Two different measurement methods which can be used to do the same thing. To guide a robot over a predefined course I would use the induction method (as long as the situation allows laying out wires), since it can be made less susceptible to noise. For that you can filter out all frequencies except of the used guiding frequency with a LC circuit. Or even better (though maybe not important) a lock-in amplifier. The hall sensor is an analog device, which can be very noisy.