Hi, I work at a shelter , or pound, for abandoned or lstray animals, usually dogs and cats and some wildlife.
You do some really great work.  What do you normally do with the animals you find in the wild.
If they are injured, our vet will come  out. While we are a no kill , it is sometimes policy to euthanize sick or dangerous.
What does euthanize mean?
Put to sleep  The US doesn't have a government run organization that provides oversight of the various types of shelters,
That is very sad.  Do you try to help the animals find a home before hand?
Many states do regulate shelters in their jurisdictions. We always try to find homes for them.
Comparatively, how many dogs vs. cats get adopted in a shelter?
still be considered a no-kill shelter.
Definition.
A no-kill or limited admit shelter is a shelter that saves healthy, treatable and rehabilitatable animals. As a benchmark, at least 90% of the animals entering the shelter are expected to be saved. The save rate must be based on all animals entering the shelter: "It does not matter if the animals are old, blind, deaf, missing limbs, or traumatized. All of these animals are worthy of our compassion, all of them
cat's life. They must eventually get another round. Capturing a feral cat can be difficult, and some caretakers do not care to take the animal to the vet again. If they do not get their vaccinations when they are due, the cats can contract diseases and spread. Cats are three to four times more likely to get rabies than other domestic animals like dogs. 
References.
http://www.takepart.com/article/2014/03/31/sorry-cat-lovers-trap-neuter-release-flat-out-doesnt-work
https://www.aspca.org/animal-homelessness/shelter-intake-and-surrender/pet-statistics
External links.
- Arizona Humane Society’s Working Cats Program
- Best Friends Animal Society: L.A.