Reading through a book of cocktail recipes from the late 1800s, I notice some recipes call specifically for Santa Cruz rum and some call for Jamaican rum. Is this a mere place of origin reference, or is there some qualitative difference? For example, would one of them be what we now call spiced rum? Or light rum vs dark rum?
If the cocktail is from the 1800's it's just the place of origin. Nowadays the two are both fairly strong rums. They taste almost the same except the Jamaican Rum (where I live) is cheaper.
The difference seems to have been smaller than that. (I'm not an expert on the subject, but I did read this page.)
You can probably use any aged rum here; light rum would probably have too little flavor and spiced rum probably wouldn't fit. Of course, it depends on the specific recipe.
The reference to Jamaica rum refers to a heavy dark rum like Meyers. Santa Cruz was a lighter bodied rum. The Jamaicans do also make light rums like Appleton.