At the left we have the Chess Knight moving from origin (black). First step is blue, second is rose, third is yellow.

At the right we have the Chess Tower moving from origin (black). First step is yellow, second is rose, third is blue.

We can see that from O-2 to O+2 (for X and for Y, where O is the origin) we can map the number of steps as 1:3, 2:2 and 3:1 for Knight:Tower. (And 4:4 in the white corners.)