Two giant galaxies can smash head-on into each other. Yet not a single one of their billions of stars will ever collide.
The difference comes down to scale. If you scaled the Sun down to the size of a ping-pong ball, the nearest neighboring star would sit more than seven hundred miles away. Shrink the entire Milky Way to the diameter of a dinner plate, however, and the neighboring Andromeda Galaxy sits just twenty feet across the room.
The Sun measures roughly 1.4 million kilometers across, whereas the distance to its closest neighbor, Proxima Centauri, is about 40 trillion kilometers. That yields a distance-to-diameter ratio of nearly thirty million to one. In the open volume of interstellar space, stars are tiny specks separated by incomprehensible expanses of empty space. Two stars traveling through a galaxy have a negligible chance of physical impact.
Galaxies, by comparison, are crowded together relative to their dimensions. The Milky Way spans roughly 100,000 light-years across, while Andromeda sits approximately 2.5 million light-years away—a separation only twenty-five times our galaxy's diameter. Drawn by mutual gravity, galaxies frequently interact, sideswipe, and merge. The Milky Way has already consumed several dwarf galaxies over its lifetime and will begin merging with Andromeda in the distant future.
During these galactic collisions, gravitational tidal forces draw stars out into long streamers, while diffuse interstellar gas clouds collide directly, compressing to trigger the formation of millions of new stars. The stars themselves simply glide past one another, continuing along newly altered orbits through the vacuum.