In the previous post, I showed how a nearby star -- Barnard's Star -- appears to move against the sky over time. Barnard's Star is the second closest to the Sun. The closest star (actually, the closest three stars, all bound into one multiple star system) is the Alpha Centauri system, at 4.3 light years away, about 2/3 the distance to Barnard's Star.
Alpha Centauri consists of three stars, two bright stars (both broadly similar to the Sun, called Alpha Centauri A and Alpha Centauri B) in a close orbit, and a third, much farther out, that is currently slightly closer to the Sun the the other two. This star, a very dim, red star, is sometimes called Proxima Centauri to emphasize its closeness to the Sun; it is the closest star to the Sun we know of.
Unsurprisingly, Alpha Centauri was one of the first stars to have its parallax measured. Since Alpha Centauri is closer to the Sun than Barnard's Star, it shows a larger parallax shift every year. Additionally, it is moving through space more slowly, so its proper motion is quite a bit lower (despite being closer). As a result, the parallax effects are easier to see with Alpha Centauri: