We study the community structure of the multi-network of commodity-specific and aggregate trade relations among world countries over the 1992-2003 period. We compare structures across products and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geographical distances and regional trade agreements. We find that: (i) plastics and mineral fuels -and in general commodities belonging to the chemical sector- have the highest similarity with aggregate trade communities; (ii) both at aggregated and disaggregated levels, physical variables such as geographical distance are more correlated with the observed trade fluxes than regional-trade agreements.