When Maribeau Lamar set up the Texas Public School System, each county when it was formed, would establish a free public school for the children of that county. This would be supervised by a County Superintendent.
An Independent School District would be one that would serve a specific area, like a town or city.
A Unified District would be where two separate districts would be united, generally crossing county lines.
A Consolidated District would be where several schools within a county school district would be consolidated into a single school district. In the case of A&M Consolidated, it would have been the school at A&M, the school in College Station, Wellborne and so on. (lower Brazos County)