What is the difference between mass and size when it comes to planets?
Same as the difference between mass and size when it comes to anything. Size is how much space something takes up, mass is how much “stuff” there is, I.e. how much it weighs.
A ton of lead and a ton of feathers have the same mass, but a ton of feathers is going to take up a lot more space.
Mass is how much stuff is there. Size is how much space it takes up.
For example, Saturn has a diameter 9x that of Earth; as a result its volume (the space it occupies) is 729x that of Earth but its mass is only 95x that of Earth.
Fun fact: Saturn is the only planet in the solar system less dense than water so if you had a gargantuan glass of water, Saturn would float on it (assuming the glass was on a body with sufficient gravity to be pulling Saturn downwards)
Are you talking about the mass and size of planets or the phenomenon that if you were to step on a certain type of scale on Mars or the moon it would display a different weight than on earth?
The first part is that planets bigger in size/volume tend to have more mass, but the relation is not linear.
Big planets in our solar system are all gas giants and have much less mass per volume than earth has, in fact the earth is the densest planet in out solar system.
The second part about hings weighing less comes from the different surface gravity on other planets and moons.
Mass is mass everywhere but weight changes with the gravity.
On earth you have a gravitational acceleration of on average 9.81 m/s², that means each second in freefall a falling object will get 9.81 meters per second faster. Due to the magic of the metric system that neatly translates into each kilogram of mass also exerting 9.81 Newtons of force on the surface it is resting on.
The exact value varies ab it by location the 9.81 m/s² aka 9.81 N/kg are only an average, the value in places like Oslo can be as high as 9.825 and as low as 9.78 in Mexico City.
Scales are supposed to measure out mass but depending on the way they do that they might actually measure the force of the gravity that mass exerts on for example a spring. This works because scales are stationary and the ratio of force to mass tends to fixed in each place.
However if you carry you scale from Scandinavia to Mexico you have to recalibrate it to show the correct value again.
With other planets like mars or the moon this effect would be much stronger. Venus is pretty close to Earth and the gravity there is about 8.87 m/s² lower than on earth but not too much so that this would be a huge problem. (The fact that your scale would be melting would be a bigger problem.)
Mars only has 3.71 m/s² on average (It gets lower if you for example climb to the top of Mount Olympos).
On the moon it is only about 1.62 m/s², which is why the astronauts that actually walked on it did those weird jumping movements despite wearing quite heavy suits.
You have the same mass everywhere you go but the weight will feel different.
This can be really weird because the momentum is not changed, it takes the same amount of force to get something moving or to stop something from moving, but it take far less force to lift something up against the pull of gravity.
Stuff will feel lighter but still be as massive as it always was.
Density of the material that the planet is made of. A large planet with mostly carbon can be less massive than a small one with mostly iron, for example.