Isabel was originally a Spanish form of Elizabeth but it was imported into France in the early Middle Ages and then into England soon after so it was routinely used amongst English speakers centuries later in the 1800's. In the late Middle Ages it was the same name as Elizabeth here in England and you'll find records where a woman was baptised Elizabeth, married as Isabel, inherited property in both names and was buried as Elizabeth with a death record listing Isabel. They used to have law cases here to decide if names were one and the same or separate and eventually the two became distinct.
US Records prior to 1900 were sometimes poorly kept, sometimes lost due to natural disasters and didn't share our modern concern with statistics. The name base was much smaller so a name in the top 10 then tended to stay there for decades and be shared by a large chunk of the population. The Latinate form Isabella was popular here in England in the 1700's and the use of Isabel as a variant of Elizabeth had been well-established by that time. So Isabel on a Caucasian woman in the 1860's doesn't indicate anything unusual - she was one of many at the time.