One key distinction in dimensional analyses is that between common factor analysis and principal component analysis. This presentation has several goals. One goal is to provide some historical background regarding the development of these two techniques, outlining key developments by the main contributors. Another is to outline similarities and differences between common factor and component analysis. In previous work, I have documented the different representations that occur with the two techniques; here I will stress the way in which assumptions about errors, or unique factors, are a basis for much of these differences. I will then discuss several misconceptions that have arisen regarding the two techniques. All of these points will be considered in connection with several of the core propositions that drove the work by Spearman and particularly Thurstone as they developed techniques of factor analysis that are a mainstay of statistical methods in psychology and the behavioral sciences.