Many types of ability tests exist, including attainment, I.Q. and aptitude tests. Aptitude tests are the type of ability test used for Graduate Selection to jobs. Aptitude tests are designed to assess your potential for acquiring and dealing with new information in order to achieve a particular solution. Ability tests were developed to identify many of the underpinning factors of general intelligence, or 'g' as it was first proposed by Charles Spearman in 1904. The idea that general intelligence consisted of more specific intelligence factors such as numerical, logical, verbal etc, was embraced and subsequent research in this field reinforced and improved our understanding of what intelligence, and consequently ability, meant. This led to the development of aptitude tests.
Today there is a vast range of aptitude tests. These include numerical reasoning, verbal reasoning, logical reasoning, diagrammatic reasoning, spatial reasoning, critical reasoning and so on. Descriptions of these are all available on this site. These tests are designed to assess an individual's innate or learned level of competence to undertake a particular task or type of work, at a given level. A variety of tests are developed for this purpose where, in the context of work, a particular competence is desired in a given area. For example, applicants for an Accountant position may be asked to complete a 'numerical' aptitude test.
It is important to note that personality assessments are not tests. Personality questionnaires identify preferences and do not tell you about an individual's ability or aptitude.