The paper deals with the comparison of defining and conceptual delineating the concepts cognitive processes, cognitive functions, and cognitive abilities. The categorization of cognitive processes on horizontal and vertical level is sketched. Three approaches to defining the concept of cognitive function in the relation to defining the concept of cognitive process are specified. The cognitive function is regarded as a task or algorithm, the cognitive process presents rather the course of the given function. The cognitive ability expresses the alternative or the quality of the process or function. The differences among cognitive processes and functions and their relations are explained on the basis of criteria of speed, visibility, and hierarchy. In the concluding part, the paper analyzes the difference between the concept of cognitive process and cognitive ability. The theoretical framework for delineation and analysis of concepts is represented besides psychology also by means of mathematics. The linguistic basis of mentioned concepts is also taken into account. The paper responds to the need to precise the terminology in the scope of breakthrough of psychological concepts into the social sciences discourses.