A spring-tooth harrow is a type of harrow, and specifically a type of tine harrow. It uses many flexible iron teeth mounted in rows to loosen the soil before planting.
A drag harrow more specifically refers to a largely outdated type of soil cultivation implement that is used to smooth the ground as well as loosen it after it has been plowed and packed. It uses many flexible iron teeth usually arranged into rows. It is set on the ground and pulled and cannot be backed up. It has no hydraulic functionality and has to be raised/adjusted with one or multiple manual levers. It was originally pulled by draft animals and later adapted to tractors. It is a largely outdated piece of farm equipment, having been replaced by more modern tillage equipment, however, smaller farmers still use them.