Why do different people pedal at difference rates (have a different cadence) on the same road at the same speed?
As Andrew says, different people have different optimum cadences.
Also, many people don't understand that there is such a thing as optimum cadence.
Optimum cadence is determined by your exercise goal.
What is the "right" cadence?
As Andy P points out, slower and harder stresses skeletal muscles, faster easier stresses heart and lungs.
If your goal is to build skeletal muscle then pedaling slower and harder is better.
If your goal is to build heart and lung endurance for long distance riding then pedaling faster and easier is better.
Low cadence riding in a hard gear taxes your skeletal muscles, specifically your quads. Since you’re using a big gear, you have to apply lots of force to turn it. If your legs are very big and powerful, this may work well for you.
Turning the big gear slowly has less effect on your heart and lungs, so you’re less likely to be gasping for air or have a skyrocketing heart rate.
However, there is an edge towards the higher cadence riding. Your heart and lungs can take repeated punishment for long periods of time (and they recovery quickly after hard efforts,) while your muscles will fatigue relatively quickly.
A high cadence also places less stress and torque on your knees. So if you have bad knees, you’re usually better off spinning faster, in a low gear
Think about it this way. How fast you go on a bicycle is related to how much power you generate.
Power = how hard you pedal x how fast you pedal(cadence)
Here's an article on how to count your cadence
So, on a flat road: (made up numbers here just as an example)
You can go 12 miles per hour pedaling 20 times a minute pedaling hard.
You can go 12 miles per hour pedaling 80 times a minute pedaling easy.
How fast you pedal at a set speed is determined by what gear you are in.
Heart and lung focused cadence
Rule of thumb: is to ride in the easiest gear that I'm comfortable with for a specific speed and then pedal at a constant cadence.
Skeletal Muscle focused cadence
Rule of thumb: ride in the hardest gear you are comfortable with for a specific speed and pedal at a constant cadence.
Mixing it up
The way I've described things it may seem like it's either pedaling hard and slow or fast and easy. I'm just trying to make the differences clear. In your riding you may decide optimal is somewhere in the middle, or you may mix fast and slow pedaling on the same ride.
Bottom line, Ride frequently and experiment to find the optimum cadence for your situation.