There is no difference between a Cro-Magnon person and a Homo sapiens because Cro-Magnon were Homo sapiens!
"The Cro-Magnon were the first early modern humans of the European Upper Paleolithic in Europe. The earliest known remains of Cro-Magnon-like humans are radiometrically dated to 35,000 before present.
The name derives from the Abri de Crô-Magnon (French: rock shelter of Crô-Magnon) near the commune of Les Eyzies-de-Tayac-Sireuil in southwest France, where the first specimen was found. Being the oldest known modern humans (Homo sapiens) in Europe, the Cro-Magnon were from the outset linked to the well-known Lascaux cave paintings and the Aurignacian culture that flourished in southern France and Germany. As additional remains of early modern humans were discovered in archaeological sites from Western Europe and elsewhere, and dating techniques improved in the early 20th century, new finds were added to the taxonomic classification.
The term "Cro-Magnon" soon came to be used in a general sense to describe the oldest modern people in Europe. By the 1970s the term was used for any early modern human the World over, as was the case with the far-flung Jebel Qafzeh remains in Israel and various Paleo-Indians in the Americas. However, analyses based on more current data concerning the migrations of early humans have contributed to a refined definition of this expression. Today, the term "Cro-Magnon" falls outside the usual naming conventions for early humans, though it remains an important term within the archaeological community as an identifier for the commensurate fossil remains in Europe and adjacent areas. An example of this is how current scientific literature prefers the term "European Early Modern Humans" (or EEMH), instead of "Cro-Magnon"."
So. Essentially they are one and the same. Cro-Magnon were Homo sapiens, just 35,000 years ago.