I don't have a Santa Maria grill. But I have a Schwenker type grill that is suspended over an open fire, can be lowered/raised, and can swing/rotate over the fire (this latter averages out hot spots).
Cooking over an open fire is more variable than using a grill/smoker. But the heat and smoke can be controlled by (1) tending the fire and (2) raising/lowering the grate.
If you let the wood burn all the way down to ashes, it is the same as grilling over lump charcoal. Or you can use variable amounts of actively burning wood, which exposes the meat to variable amounts of smoke. Since there is no lid, the meat may not absorb as much smoke as when using a smoker. But wood combusted in an open fire has a somewhat different profile of byproducts, which imparts a slightly different smoke flavor. Also, there is a roasted flavor component, which is usually absent from smokers.
IMHO, meat cooked over an open fire has a smokey flavor, but it depends on how the cook was done. It sometimes may not seem as strong as cooked in a smoker, but the combination of smoke and roasted flavors are hard to beat.