That's a really cool video! While the visuals are symbolic, the planets do have very different compositions.
Planets in our solar system generally fall into three main groups: terrestrial, gas giants, and ice giants.
The rocky, terrestrial planets like Earth, Venus, and Mars have a solid surface, a silicate mantle, and a core made mostly of metals like iron and nickel.
Gas giants, like Jupiter and Saturn, are mostly made of hydrogen and helium with a heavier core, similar to the elements that make up stars.
Then you have the ice giants, Uranus and Neptune, which have a small rocky core surrounded by a thick layer of icy materials like water, ammonia, and methane.