My ancestors were descended from people who arrived in French and Spanish Louisiana. Many were freed during that period and others after the Louisiana Purchase. All were called "gens de coleur libre", "de coleur libre", femme de coleur libre[if they were women]. Other labels denote physical descriptors[not RACIAL ones] like "negresse libre" or "quatrone libre". So, I don't see much of a difference between "freed" and "free born" unless you refer to the post-Civil War years.
Being that my paternal ancestry is Louisiana Creole, the society, history, and cultural dynamics were born akin to Latin societies[Cuba, Brazil,Haiti, Puerco Rico] then say Anglo-American societies[Ie New England or Anglo-American South]. A lot of times when Historians or researchers discuss Louisiana, they tend to view it from an Anglo-American lenses instead of a Latin one. There were no "segregated" communities of free persons of color and Native Americans in Louisiana like the ones in the Anglo-American world. I've several examples of early censuses of "mixed neighborhoods" in Louisiana. Many of my Louisiana ancestors had a much higher status in their societies then FPOC in the Anglo-American world. Some owned slaves and others were bankers to White louisianians. Social relations were very open. "Mixed" marriages were sanctioned from time to time[I've several relatives like this] well into the early 20th century. And many after the war intemarried with descendents of fpoc and well as a few "freed" slaves[both Anglo and Louisiana Creole]. So, in my case, I have ancestors who freed as early as the 1750s and as late as 1847 who were called "fpoc" regardless.