Why distance makes star motion invisible to the eye
The apparent motion of an object across the sky depends on how fast it actually moves and how far away it is. The Moon orbits Earth at a distance of roughly 384,000 kilometers, so its motion translates into a large, obvious sweep across the sky each night. Stars sit at distances measured in light-years, so even genuinely fast motion projects onto the sky as a tiny angular shift. Astronomers call this apparent angular movement "proper motion," and it is measured in milliarcseconds per year — a milliarcsecond is about the width of a coin seen from several kilometers away.
A survey using infrared sky data found newly identified nearby stars with proper motions greater than 0.5 arcseconds per year, and only ten of those exceeded 1 arcsecond per year [2]. For comparison, the full Moon spans about 1,800 arcseconds across. Even the fastest-moving stars in that survey shift by less than a thousandth of the Moon's width in a year, which is why they appear pinned in place to anyone watching casually.
Stars are not actually fixed — they just move slowly on our sky
The impression of a motionless sky is an illusion of scale, not a fact about the stars. Large surveys routinely measure proper motions for thousands of stars. One study tracked the proper motions of 4,199 massive O and early B stars in the far Carina Arm of our galaxy, at distances mostly beyond 4 kiloparsecs, and found patterns in their motion that recur over roughly 2–3 degrees of galactic longitude [3]. That is real, measurable movement — it is simply spread over enormous distances and long times.
The same study also identified a moving group of more than 50 OB stars and estimated that at least 10 percent of the sample are "runaway" stars, ejected from clusters such as NGC 3603 and Westerlund 2 during intense spells of ejection between roughly 0.5 and 0.9 million years ago [3]. These stars are traveling fast by any standard, yet their motion across our sky remains a slow crawl because of how far away they are.
The small wobble Earth's own orbit adds
There is a second, subtler kind of apparent stellar motion: as Earth travels around the Sun, nearby stars appear to shift slightly against more distant ones, an effect called annual parallax. This is the same effect you see when you hold a finger up and alternate closing each eye — the finger seems to jump against the background. For stars, the jump is minuscule. One measurement of the Mira variable star BX Camelopardalis used radio interferometry to pin down its parallax and its systemic motion [4].
The history of this measurement is telling: annual stellar parallax was not successfully detected until 1838, when Friedrich Bessel measured it for the star 61 Cygni, after many earlier failed attempts [5]. The effect is so small that it took centuries of effort to confirm. A parallax measurement for a nearby dwarf star in the southern survey gave 276 milliarcseconds, corresponding to a distance of about 3.6 parsecs [2] — a tiny angular shift for a relatively close star, and far smaller for anything more distant.
What this means for someone watching the sky
Over a single night, the Moon moves noticeably against the stars because its orbital motion is fast and it is close. The stars themselves shift by amounts far below what the eye can resolve in that time. Over many years, careful measurements can reveal stellar motion, and the fastest nearby stars do change position measurably on photographic plates and in survey data [2]. But to a casual observer, the stars form a stable background against which the Moon, planets, and artificial satellites move.
So the short answer to why stars don't move like the Moon is not that stars are stationary. It is that their real motions, while often substantial in absolute terms, are projected across such vast distances that the angular shift is tiny — and the additional parallax wobble from Earth's orbit is smaller still [4][5]. The sky is full of motion; most of it is just too slow and too distant for our eyes to catch.
Sources used in this answer
An Attempt to Measure the Annual Parallax or Proper Motion of Four Radio Stars
The paper investigates measurement of annual parallax and proper motion of radio stars, addressing stellar motion but not comparing it with lunar motion.
Southern Infrared Proper Motion Survey I: Discovery of New High Proper Motion Stars From First Full Hemisphere Scan
An infrared proper motion survey discovered 72 new nearby stars with proper motions greater than 0.5 arcseconds per year, ten exceeding 1 arcsecond per year, and measured a parallax of 276 milliarcseconds for one dwarf star.
Proper motions of OB stars in the far Carina Arm
Proper motions of 4,199 O and early B stars in the far Carina Arm show a recurring saw-tooth pattern and reveal a moving group plus an incidence of runaway O stars of at least 10 percent.
Annual parallax measurement of the Mira variable star BX Camelopardalis with VERA
The paper measures the annual parallax and systemic motion of the Mira variable star BX Camelopardalis using radio interferometry.
Seeing Earth's orbit in the stars: Parallax and aberration
The paper describes the historical discovery of stellar aberration and annual parallax, noting that Bessel first measured stellar parallax in 1838 for 61 Cygni after earlier failures.