Ha well I was wrong. According to Stellar, here's how it works:
You’re totally right to flag the confusion—two different kinds of “size” got mixed.
What “400×” really means
Diameters:
Sun ≈ 1,392,700 km
Moon ≈ 3,474 km
Sun/Moon diameter ratio ≈ 1,392,700 / 3,474 ≈ 402 → “~400× bigger (in diameter)”
Distances (from Earth):
Sun ≈ 149,600,000 km
Moon ≈ 384,400 km
Sun/Moon distance ratio ≈ 149,600,000 / 384,400 ≈ 389 → “~400× farther”
Because apparent size ≈ physical diameter ÷ distance, those two ~400s nearly cancel, so the Sun and Moon look about the same size in the sky—hence total/annular solar eclipses.
Where the “1.3 million Earths” fits
“You can fit ~1.3 million Earths inside the Sun” refers to volume, not diameter.
Volume scales with the cube of diameter. If something is ~400× larger in diameter, its volume is about 400³ ≈ 64 million times larger.
Actual numbers:
Sun/Earth volume ≈ 1.3 million
Sun/Moon volume ≈ ~65 million (consistent with ~400× diameter difference)
Moon vs Earth (to address the “Jupiter-sized Moon” worry)
Moon is ~27% of Earth’s diameter and ~1/81 Earth’s mass.
Jupiter is ~11.2× Earth’s diameter and ~318× Earth’s mass—completely different scale.
So the “400× smaller” claim is not saying the Moon is 1/400 the Sun’s volume or that it’s Jupiter-sized; it’s specifically about diameter relative to the Sun, paired with distance.
Quick angular-size check (why eclipses work)
Sun: 1,392,700 / 149,600,000 ≈ 0.00931 rad ≈ 0.533° (~32 arcmin)
Moon: 3,474 / 384,400 ≈ 0.00904 rad ≈ 0.518° (~31 arcmin)
Those overlapping ranges are why sometimes the Moon exactly covers the Sun (total eclipse) and sometimes leaves a ring (annular), depending on perigee/apogee.
Bottom line:
“~400× smaller and ~400× closer” is a good rule of thumb for diameters and distances, which explains eclipses. The “1.3 million Earths” is about volume, so it doesn’t contradict the 400× diameter fact.