Most people would say that Jamaican jerk sauce is African since the origins of jerk pork can be traced back to the pre-slavery days of the Cormantee hunters of West Africa. When the British invaded Jamaica in 1655 the Spanish colonists fled, leaving behind a large number of African slaves. Rather than be re-enslaved by the British, they escaped into Jamaica's mountainous regions where they mixed in with the local Taínos.
Though Jamaican jerk sauce certainly was derived from African ancestry, it is something that was adapted and modified over hundreds of years as various cultures added their influence. From the start, changes had to be made since the Cormantee slaves found themselves in new surroundings on the island of Jamaica and were forced to use what was available to them.
As a result, there was naturally a departure from some of the original spices used in jerk and new ingredients were added or substituted as necessary. One new addition to the recipe was the Scotch bonnet pepper, which is largely responsible for the heat found in Caribbean jerks. The Scotch bonnet is one of the hottest chile peppers around with a heat level similar to the habanero pepper.
Caribbean jerk often provides a blast of heat that follows with a tangy, vinegar taste. However, a sauce that uses authentic African ingredients has a very different flavor. African jerk provides a layered pallet of flavor. Rather than focusing on heat, the more traditional recipes offer a selection of spices that really enhance the taste of whatever the sauce is added to.
Another difference between the two sauces is in their composition. Jamaican jerk sauce is designed to be a marinade so it is much thinner with an "oil and water" type of consistency while an authentic African sauce tends to have a thicker, smoother body which gives it much more versatility in the kitchen. As an example, it is thick enough to be brushed onto meats on the grill. Try that with a marinade and you will find that the majority will simply run off because it is so thin.
Truly, traditional African jerk sauce differs from Jamaican jerk in flavor, composition and application.