In volcanology, spatter refers to any tephra (matter thrown out from the volcano) that is still molten or semi-molten when it hits the ground. Spatter usually looks like globs of tar splashed on the ground, caught in trees, or piled into mounds. It is a very descriptive term.
Spatter may be found as individual spatters of rock, but usually you find it referred to as part of a formation. If you get enough spatter to layer on itself you have welded spatter (AKA spatter agglutinate or simply agglutinate). When you get even more spatter, it starts forming cones. Some volcanic cones are made up primarily out of spatter, and are called spatter cones. If these cones contain large amounts of other tephra (cinders, scoria, lapilli) glued together with spatter, they may be referred to as spatter and cinder cones. These s&c cones tend to be the result of longer eruptions which have varied intensity over time.
Spatter cones are larger cones forming around a volcanic vent. Smaller spatter cones may be formed around holes in the crust covering a lava flow, where the lava splashes out in droplets and gobs. This results in small cones, pillars, and mounds of spatter called hornitos (small, yes, but still often taller than a grown man).
When a volcanic vent is in an elongated fissure, it may form spatter ramparts on either side of the fissure, rather than a spatter cone; these are basically the same formations as spatter cones, but not cone-shaped.
The term spatter does not indicate any specific size range or mineral composition of the rock, although basaltic (mafic) formations are more common than felsic.