Open Admission Shelters...
...are shelters that don't turn away any animal based on their age, breed, health, behavior, or aggression. "No Kill" or "Limited Admission" shelters can pick and choose which animals they will accept and how many. Unlike limited admission shelters that euthanize animals as a means of population control, open admission animal shelters only put animals to sleep that are extremely sick, suffering or unable to be rehabilitated enough to be adopted. However, that doesn't mean some animals aren't euthanized after being admitted to the shelter...
"No Kill" Shelters...
"...the most common understanding of a no-kill shelter isn't that it never kills, though that's clearly what it implies. Instead, it's a shelter with a 90 percent “live release rate” — meaning that nine of every 10 animals admitted leaves alive."
Many shelters rely on foster homes to keep pets until they have room, and some rescue groups are run entirely through foster care. While most people choose to foster dogs or cats, there are also rescues for hamsters, rabbits, horses, and other animals.