When you talk about rate, you will expect that it will be in terms of a time unit. It measures how fast it is going. So, you would expect that the denominator is in time units. For the movement, you can measure this with either distance or velocity.
So, for the first variety, you would need distance and time to measure the rate of how far you go at a certain time. It is also called as velocity. For the second variety, you would need velocity and time to measure the rate of how fast you are going at a certain interval. It is also called as acceleration.
