Answer: 840

Solution:

Write the digits as $a,$ $ar,$ $ar^2.$ For the largest geometric number, take $a = 9.$ An integer ratio at least $2$ would push the next digit past $9,$ and $r = 1$ repeats digits, so $r$ is a fraction whose denominator squares into $9:$ the choices $r = \frac{2}{3}$ and $r = \frac{1}{3}$ give $964$ and $931.$ The largest is $964.$

For the smallest, take hundreds digit $1.$ Then the tens digit $r$ must be an integer at least $2$ (the digits are distinct), and $r = 2$ gives $124,$ which beats $r = 3$'s $139.$

The difference is $964 - 124 = 840.$