In theory, ability and achievement tests are measuring different things. In practice, an individual's performance on one type of test usually is strongly correlated with his performance on the other, and occasionally there have been disputes about whether some standardized ability tests are actually measuring achievement. Tests for ability are usually normed, which means data have been collected from the results of the tests with enough subjects to give researchers sufficient information to determine a mean and standard deviation. These measures allow them to compare an individual's performance with students across the country. This is not necessarily true for achievement tests, which may be developed locally, or by teachers.
From a policy standpoint, interindividual differences in ability and achievement may be important if they indicate problems in the educational system. If significant differences in test scores show up when comparing groups--for example, differences by race or socioeconomic status or location--then educators and policymakers may want to look at teaching methodologies or other factors that may be interfering in educational achievement. If the differences seem to be geographically based, policymakers may consider whether funding is an issue and search for remedies to these inequalities.
Sometimes interindividual differences in ability and achievement are evidence of special educational needs. Ability scores that are two standard deviations below the mean are taken as evidence of a cognitive impairment and may qualify the student for special services in most states if other requirements are met. At the other end of the scale, students that perform significantly better then average on ability and achievement tests may qualify for academically gifted programs in some school systems.
Intraindividual differences in ability and achievement are often more interesting to educators than interindividual differences. Until recently, differences of greater than one standard deviation were taken as evidence of an existing learning disability. In addition, testing results that show significant differences in achievement by subject area may indicate the need for differentiated instruction, since individual students have different learning styles.