I have found an explanation of two injections
Animal euthanasia - Wikipedia, the free encyclopedia
Pets are almost always euthanized by intravenous injection, typically a very high dose of pentobarbital or sodium thiopental. Unconsciousness, respiratory then cardiac arrest follow rapidly, usually within 30 seconds.[2] Observers generally describe it as a quick and peaceful death.
Some veterinarians perform a two-stage process: An initial injection that simply renders the pet unconscious and a second shot that causes death.[citation needed] This allows the owner the chance to say goodbye to a live pet without their emotions stressing the pet. It also greatly mitigates any tendency toward spasm and other involuntary movement (i.e., the pet's facial or eye movement) which would tend to increase the emotional upset that the pet's owner is already experiencing.