Is supply current lower than output current in voltage regulator circuits?
A linear voltage regulator acts pretty much like an intelligent resistor setting it's value in such way that the voltage behind it is regulated to the wanted voltage.

Because of that, the current at the input is almost the same as the current of the output. It will be higher because the linear regulator needs some current as well to do its thing.

This also means, that a linear voltage regulator is wasting all the energy to heat, which in your case would turn to be a whopping 380W ((Vin-Vout)*Iin), so that would be a really beefy linear regulator and require a lot of cooling. I'd say it's very impractical.

For a case like that a switching regulator will probably be the better choice, as it converts the voltage with a certain efficiency. In good designs it can be very high, 90% or higher is achievable. That means that the input power is higher than the output power but the current would be lower (for a step down converter):

$$ \eta = \frac{P_{out}}{P_{in}} \rightarrow P_{in} = \frac{P_{out}}{\eta}$$

In your example with 90% efficiency the input power would be just 111W (instead of 480W for the linear regulator). And the current on the 24V side would turn out to be just 4.63A.

Switching regulators have their downsides as well, like a higher output voltage ripple.