The process of natural selection acts both on individual organisms within a population and on individual cells within an organism as they develop into cancer. In this work, we have taken a first step toward understanding the differences in selection pressures exerted on the human genome under these disparate circumstances. Focusing on single amino acid substitutions, we have found that cancer-related mutations (CRMs) are frequent in evolutionarily conserved sites, whereas single amino acid polymorphisms (SAPs) tend to appear in sites having a more relaxed evolutionary pressure. Those CRMs classed as cancer driver mutations show greater enrichment for conserved sites than passenger mutations. Consistent with this, driver mutations are enriched for sites annotated as key functional residues and their neighbors, and are more likely to be located on the surface of proteins than expected by chance. Overall the pattern of CRM and polymorphism is remarkably similar, but we do see a clear signal indicative of diversifying selection for disruptive amino acid substitutions in the cancer driver mutations. The ultimate consequence of the appearance of those mutations must be advantageous for the tumor cell, leading to cell population-growth and migration events similar to those seen in natural ecosystems.