Also how much short-term inaccuracy there is depends on the type of oscillator used. An OCXO will (usually) have less short-term jitter and better stability with ambient temperature changes than a chip-scale atomic clock module, but will drift more than the atomic clock long-term. The really expensive setups combine various clocks to maximize stability over all the durations of interest & minimize influence from various external factors (temperature, humidity, barometric pressure, external magnetic fields, other EMI, gravitational bias, etc.).
Gravitational bias is a really fun one since you can easily demonstrate it & its' not immediately obvious. Take a quartz oscillator, and a reference oscillator. Measure the frequency of both. Turn the quartz oscillator on its side. The phase (and usually also frequency) will change: the physical quartz has inertia & gravitational mass, so changing its orientation changes how it oscillates. In one orientation the movement of the quartz atoms is perpendicular to the force of gravity, so both directions of oscillation are biased the same amount. In another orientation one the movement of the quartz atoms is parallel to the force of gravity, so the part of the crystal moving down accelerates a bit more than the part of the crystal moving up.