The development of a "normal cell" into a "cancer cells" is not a sudden, one-step phenomenon.
There exists a series of changes that are known to occur in normal cells that gradually turns them to cancer cells. These changes have been given names like "atypia", "dysplasia", "pre-malignant" etc by pathologists.
Several "pre-cancer" states have been identified by doctors and scientists by careful observations over the last several decades. These are conditions in which the chances of developing full-blown cancer are higher than in a normal person. They include dysplastic cells identified in pap smears, Barrets esophagus identified on endoscopy, leukoplakia of mouth etc.
You can think of a pre-cancerous cells as lying somewhere in the middle of the spectrum, where a "normal" cell is at one end, and "cancer" cell is at the other.
Thank you so much for answering this question for me. It makes sense to me now.