General transcription factors help to turn on many genes in most or all situations while specific transcription factors help to cause necessary time- and place-specific changes in gene expression.
Work Step by Step
Think about the cells in your fingertip. They have to express some genes in common with all other cells just to stay alive, such as ones for cellular respiration. Other genes, to make those cells to look and function appropriately (as in making fingerprints), must be expressed just in those cells. The two sets of transcription factors mentioned in the question achieve these two aims.