Difference in positive or negative lymphocytes?

Positive
Double-positive  move deep into the thymic cortex where they are presented with self-antigens (antigens that are derived from molecules belonging to the host of the T cell) complexed with MHC molecules on the surface of cortical epithelial cells. Only those thymocytes that bind the MHC/antigen complex with adequate affinity will receive a vital "survival signal." Developing thymocytes that do not have adequate affinity cannot serve useful functions in the body; the cells must be able to interact with MHC and peptide complexes in order to effect immune responses. Therefore, the other thymocytes with low affinity die by apoptosis (programmed cell death), and their remains are engulfed by macrophages. This process is called positive selection.

Whether a thymocyte becomes a CD4+ cell or a CD8+ cell is also determined during positive selection. Double-positive cells that are positively selected on MHC class II molecules will become CD4+ cells, and cells positively selected on MHC class I molecules become CD8+ cells.

Note that this process does not remove from the population thymocytes that would cause autoimmunity or a reaction with one's own cells. The removal of such cells is dealt with by negative selection, which is discussed below.


Negative
Thymocytes that survive positive selection migrate towards the boundary of the thymic cortex and thymic medulla. While in the medulla, they are again presented with self-antigen in complex with MHC molecules on antigen-presenting cells (APCs) such as dendritic cells and macrophages. Thymocytes that interact too strongly with the antigen receive an apoptosis signal that causes their death; the vast majority of all thymocytes initially produced end up dying during thymic selection. A small minority of the surviving cells is selected to become regulatory T cells. The remaining cells will then exit the thymus as mature naive T cells. This process is called negative selection, an important mechanism of immunological tolerance that prevents the formation of self-reactive T cells capable of generating autoimmune disease in the host.