Biological process

cytotoxic T lymphocyte selection, cytotoxic T-cell selection, cytotoxic T-lymphocyte selection

The process in which a relatively unspecialized T cell acquires specialized features of a cytotoxic T cell.

cytotoxic T cell development

Note that immunologists typically use the word 'development' to refer to cells of B or T cell lineages undergoing the process that GO describes as 'cell differentiation'.