There are two types of GRE (Graduate Record Examination)

GRE General Test and
GRE subject Test

GRE is administered ETS (Educational Testing Service) an autonomous private organisation.

The GRE General Test is a required test for most American graduate schools ( Admission to business schools, require the GMAT, and law schools, require the LSAT). 

General Test measures critical thinking, analytical writing, verbal reasoning, and quantitative reasoning skills that have been acquired over a long period of time and that are not related to any specific field of study. The GRE General Test consists of multiple-choice sections on, Quantitative, Analytical and Verbal Reasonning, and a essay section called the Writing Assessment, which is taken separately. 

Verbal & Quantitative sections of General Test are Computer Adaptive Test (CAT)

The GRE Subject Tests gauge undergraduate achievement in eight specific fields of study and can help forecast a candidate's potential for success in graduate school. Each Subject Test is intended for students who have majored in or have extensive background in that specific area