Genus (pluralgenera) and species had been employed by naturalists for over a hundred years before Linnaeus, and order, class, and family in their biological senses all came into use in the 1750s and 1760s. But phylum wasn't coined until 1876 (by the German Ernst Haeckel), and family and order were treated as interchangeable until early in the twentieth century. For a time zoologists used family where botanists placed order, to the occasional confusion of nearly everyone. (To illustrate, humans are in the domain eucarya, in the kingdom animalia, in the phylum chordata, in the subphylum vertebrata, in the class mammalia, in the order primates, in the family hominidae, in the genus homo, in the species sapiens. Some taxonomists employ further subdivisions: tribe, suborder, infraorder, parvorder, and more.)
Linnaeus had divided the animal world into six categories: mammals, reptiles, birds, fishes, insects, and "vermes," or worms, for everything that didn't fit into the first five. From the outset it was evident that putting lobsters and shrimp into the same category as worms was unsatisfactory, and various new categories such as Mollusca and Crustacea were created. Unfortunately these new classifications were not uniformly applied from nation to nation.