裤带 specifically means the belt or drawstring built into trousers. For a separate leather belt (the kind you buy in a store), 皮带 (pídài, 'leather belt') is more common. Idiomatic 勒紧裤带 'tighten one's belt' = endure hardship/cut spending.
culture
Shaanxi has a famous noodle dish called 裤带面 (kùdài miàn, 'belt noodles') — wide, flat noodles as broad as a trouser belt, a regional pride of Xi'an cuisine.
