The quantitative trade literature often does not distinguish between tariffs and iceberg trade costs. This paper explores qualitatively and quantitatively how this distinction matters for the gains from trade. Most obviously, tariffs generate government revenues, while icebergs do not. In models of monopolistic competition, they may also affect entry. Finally, depending on whether they are modeled as cost or demand shifters, tariffs may have different implications on profits, entry, and, in turn, on the elasticity of trade flows and welfare. We show that the welfare formula by Arkolakis, Costinot, and Rodriguez-Clare (2012) requires qualification, even in the simple singlesector case. We find that the quantitative welfare consequences of cost- versus demand-shifting tariffs can be important.