It was both. Check you facts.
OK. Nope, Fort Sumter was never used as a tariff collection point (although curiously the Mises and Marxist websites claim otherwise).
Tariffs at Charleston were collected at the the Exchange and Customs House, located at 122 E. Bay Street in Charleston. Amazingly, it's usually considered a better idea to collect tariffs at a location near the docks where ships are actually unloading, rather than at a remote island with only a small dock in the middle of the bay.
The Grady McWhiney collection at McMurry University could
settle the question. Here is a link to their site. It is one of the largest collections of period documents in existence.
http://www.mcwhiney.org/collect/collection.html