I learned that there are two distinct sets of FIPS codes (if you don't know what a FIPS code is, all that matters here is that it should be unique and consistent). One of our data sources was consistent with the Tract geometries, and had Tract names like "Census Tract 1001, Fairfield County, Connecticut". The other had different codes, and names like "Census Tract 1001; Greater Bridgeport Planning Region; Connecticut"
Argh. (3/?)