Final answer:
The term for a rock with broken clasts in a finer matrix is 'breccia', which is distinguished by its angular fragments, as opposed to 'conglomerate' with rounded clasts, or 'sandstone' with sand-sized particles.
Step-by-step explanation:
The geological term used to describe a rock composed of broken clasts in a finer-grained matrix is breccia. Unlike sandstone, which is a clastic sedimentary rock composed of sand-sized minerals or rock fragments, breccia consists of larger, angular fragments embedded in a finer matrix. This can be contrasted with conglomerate, which also consists of larger fragments, but they are rounded instead of angular. Both breccia and conglomerate are considered clastic rocks, which are composed of geologic detritus including minerals and rocks and are part of the sedimentary rock family alongside sandstone, shale, and others.