Small Language Model
A language model at the small end of the size scale, with few enough parameters to run on more modest hardware. "Small" is a loose, relative term: the rough idea is "runnable on consumer hardware," not a hard parameter count, and "consumer" hardware can mean anything from a laptop to a several-thousand-dollar GPU. Small models are usually open-weight, so a community can download one, run it offline, inspect it, and fine-tune it for a specific task.
Being small makes a model easier to run locally, but the two are not the same: smallness is about size, locality is about whose infrastructure runs it. The trade-off with size is capability, since a small model is generally less fluent and knowledgeable than a large one, but for many tasks it performs perfectly well, with advantages in environmental impact, cost, and data sovereignty.