For a UPS you want to know both the max wattage of the load, as what % of the total output that the UPS's inverter can put out at any given time, and also the nominal steady-state watts so that you can calculate the Watt-hours, which is what will determine runtime on a given battery size.
If you have a UPS with, for example, 4 x 12V 8Ah AGM batteries, it has a certain amount of Wh you can realistically use before you deep-discharge the batteries into severe damage.
Indeed. Depending on the intended use of the UPS though, the energy capacity might not matter all that much. For a 3D printer, it seems like an UPS would be in place to weather the occasional hiccup in utility power. Utility power interruptions seem inherently bimodal. Either it glitches out for a few seconds and comes back, or it's out for hours. Pretty much any UPS will have enough energy to run a 3D printer for a few seconds or minutes, but very few UPSes exist that would run one for hours on end.
Taking that use case to the extreme, maybe someone lives in an area with very unreliable utility power. They might absolutely need to have enough energy stored to run their 3D printer for an entire print. Maybe they solve that with lots of batteries, but in many places with unreliable utility power, it's more likely they're just going to fire up a gas powered generator whenever the power goes out. Once again, the UPS only needs to last long enough for someone to notice and fire up the generator.
Folk certainly might have more exotic use cases. Maybe someone lives completely off-grid and powers their 3D printer off of solar panels, and a generator isn't a sustainable option. They'll definitely be more interested in energy capacity.
The power capacity seems important no matter what, since exceeding it will either result in a voltage brownout, tripping of a protection circuit, or melting something.
If you have a UPS with, for example, 4 x 12V 8Ah AGM batteries, it has a certain amount of Wh you can realistically use before you deep-discharge the batteries into severe damage.