The critical difference between achievement and aptitude tests is the way the criteria assess previously learned material. The achievement test explicitly examines the test taker's knowledge and memory of the content already learned. However, the aptitude test essentially disregards the test taker's ability to remember already learned material.
Aptitude tests focus more on the person's future potential, rather than facts and information memorized. Achievement tests are intended to survey the test taker's knowledge of a specific subject. There are both standardized and formal achievement tests. Aptitude is more about the potential for learning later in life.