ASHES RETURNED CREMATIONS
Method - An individual pet is kept separate from those of other pets in the cremation chamber.  The process is usually completed in one or two hours and results in a quantity of ash and fragments of bone, which are processed and returned to the owner in a temporary container or special urn. Cremated remains are odorless and can be stored indefinitely. Their weight and amount will vary depending on the pet's overall body structure. Urns (permanent receptacles specially made to hold cremains) are available in a wide variety of styles, shapes, sizes and materials. 
Advantage -  Separate cremation offers you more flexibility than other options. It allows the individual time to determine the best method of memorialization. Cremains can be easily buried in a special place, scattered in a meaningful area, or placed in an urn. The choice is yours.  You can choose to view your pet prior to cremation, and you can ask to be present while your pet is cremated.
Disadvantage - Separate cremation is more expensive than a communal cremation.

COMMUNAL CREMATIONS
A commonly used option and a sensible one if you do not wish to have your pet's cremains returned to you.
Method -Together with other pets, your pet is reduced to mineral form by exposure to intense heat. Thus your pets remains, properly termed "cremains", are co-mingled with those of several other pets.
Advantage - Economical means of cremation. Cost is relatively low when compared with separate cremation.
Disadvantage - Since cremains are co-mingled, it will not be possible to separate one pet's cremains from those of another, so you'll never have access to your pet's cremains, no matter how much you may wish to have them later.