Final answer:
Cats and dogs are considered part of the same group at the Order level, which is Carnivora, with differences emerging at the Family level.
Step-by-step explanation:
In the hierarchical taxonomic classification system, cats and dogs are considered to be part of the same group starting at the Order level, specifically the Order Carnivora. This group is characterized by organisms that have a diet primarily of meat, though not all members are strict carnivores.
Within the Order Carnivora, cats and dogs are further they are subdivided into the different Families, with cats are belonging to the Family Felidae and dogs to the Family Canidae, highlighting their differences at the more specific taxonomic levels.