In taxonomy,
Order is an assemblage of a group of related families having more number similarities, For example, Dog and Cats. They both belong to the Order - Carnivora.
On the other hand, Class is an assembly of related orders or group have a lesser number of similarities. For example, Order- Rodentia (Rat) and Primata (Human, monkey, gibbon) belongs to the same class Mammalia due to the presence of hair on the body and mammary glands