Transformers Energon was the terrible English dub of Transformers Superlink, which wasn’t that good to begin with. One infamous line of dialogue from it was “We warped into another galaxy on the outer reaches of the solar system.”.
That’s an extreme example of an issue that a lot of other anime have to a lesser degree; mixing up astronomical terms and/or the scale associated with them. Several series have used “galaxy” like it meant “universe”. Others don’t seem to realize how close a “moon” and a “planet” can be in scale.
Despite all the impossible things happening in the series, Gurren Lagann is pretty good about keeping scale consistent…until the scale becomes literally astronomical. Chouginga Gurren Lagann is the size of the moon. Tengen Toppa Gurren Lagann towers over galaxies. But in the final attack where Gurren Lagann’s forms come out of each other matryoshka style, TTGL seems more like the size of a small star or large planet. (Note; TTGL has an official size, and it’s consistent with the part with the galaxy shurikens, not the final attack. 10 million light years.)
So here we go. For starters, the difference between a planet and a moon is that a planet orbits a star and a moon orbits a planet. It has nothing to do with size, aside from the fact that a planet has to be considerably larger than its own moons; Ganymede, a moon of Jupiter, is larger than the planet Mercury. (And there’s no reason a planet the size of Jupiter couldn’t even have a moon the size of Earth.) Earth’s own moon is large enough that it could be considered a planet if it were in a different orbit, and for example, the moon and Earth are closer together in size than Earth and Jupiter are.
The Solar System consists of the sun and all the planets, moons, asteroids, comets, etc. that orbit it. Using it as a generic term to refer to similar systems around other stars is sometimes done but not really formally correct. But at least that isn’t particularly confusing, unlike when people get “solar system” and “galaxy” mixed up.
Distances between stars are measured by the amount of time it takes light to travel from there to here. For comparison, Earth is about 8 light minutes from the sun, and the outer planets are a few light hours away. The nearest star other than the sun is over 4 light years away. The Milky Way galaxy consists of over 200 billion stars (most of which likely have their own planets) and is over 100,000 light years across. (The stars are much closer together toward the center of the galaxy than in the outer parts where we are.) So, at the risk of understatement, a galaxy is far larger than “the solar system”.
And of course there are billions of galaxies in the universe.