When you arrange a cremation you'll usually be asked to choose between private and communal cremation. The main difference is whether your pet is cremated individually and whether you receive ashes back.
Private (individual) cremation
Your pet is cremated on their own and the ashes returned to you are your pet's alone. This is the option to choose if keeping the ashes matters to you. It costs more than communal cremation and is usually priced by your pet's weight.
Communal (shared) cremation
Your pet is cremated together with other pets. Because the ashes cannot be separated, they are generally not returned. This is usually the most affordable option and is chosen by people who don't wish to keep ashes.
A note on terminology
Terms aren't fully standardised across the industry. Some providers also offer an 'individual' or 'partitioned' cremation that sits between the two: pets are cremated in the same chamber but kept separate. If getting only your pet's ashes back is important, ask the provider exactly how their process works and what they guarantee.