In astronomical terms, the closest stars to the Sun are part of the Alpha Centauri system. The Alpha Centauri system consists of three stars: Alpha Centauri A, Alpha Centauri B, and Proxima Centauri. Proxima Centauri is the closest of the three stars to the Sun.
The distance between the Sun and Proxima Centauri varies over time due to the complex motions of stars in the galaxy. However, on average, Proxima Centauri is located about 4.24 light-years away from the Sun. To put this into perspective, one light-year is approximately 5.88 trillion miles (9.46 trillion kilometers).
As for how often stars come close to the Sun, it depends on the specific star and its trajectory. Most stars in the galaxy have their own distinct paths and orbits around the center of the galaxy. Close stellar encounters are relatively rare because the distances between stars are enormous on a cosmic scale. However, over extremely long timescales, some stars may pass relatively close to the Sun due to the gravitational interactions between stars and the overall dynamics of the galaxy. These encounters can be separated by millions or even billions of years.