As far as i'm concerned, America (the continent) is build up by four regions:
1. north america (canada, united states of america, united states of mexico)
2. central america (belize, guatemala, honduras, el salvador, nicaragua, costa rica, panama)
3. the caribbean islands (bahamas, cuba, cayman island, jamaica, turks and caicos island, haiti, dominican republic, *puerto rico, britosh virgin island, us virgin island, antigua, st kits and nevis, antigua y barbuda, montserrat, guadalupe, dominica, martinique, st lucia, barbados, st vincent and the granadines, trinidad y tobado, bonaire... )
4. south america (colombia, ecuador, peru, chile, argentina, Bolivia, aruba, venezuela, guyana, surinam, french guyana, brasil, paraguay, uruguay and the malvinas islands)
Countries are grouped in regions by their importance or proximity. That is why you can find in some books "central american and the caribbean".
I live in honduras and i like to be considered as "central american" as most people from central america do too.