I believe Humane Society and SPCA aren't as strictly defined as you are saying, as individual shelters operating under that name are not affiliated with each other, with the Humane Society of the United States, or the ASPCA.
Anyway, I've been volunteering with a shelter named the humane society for about 3 years. We are an open door shelter. This means that no animal brought to our door is ever turned away. We are, then, of necessity, not a no-kill shelter. However we do not euthanize animals on a time limit, and do everything possible to euthanize as few animals as possible.
We operate a low-cost spay and neuter clinic. We have humane investigators who rescue abused dogs, puppy mill dogs, etc. We have monthly food giveaways for low income people, regular low cost vaccination clinics, even low cost grooming days. We offer behavioral support for new adopters. We have an extensive foster network to enable us to care for as many animals as we can. We periodically run "specials" to try to encourage people to adopt (Currently, adoption fees on our adult cats are waived until the end of the month, and on Black Friday all dogs will have their adoption fee cut in half. Dogs 6 or older are always available to seniors 60 or over for $15.) This despite the fact that our usual adoption fee covers less than half of the usual cost of caring for an animal until it is adopted. All our animals are spayed/neutered, microchipped, vaccinated, heartworm tested and started on prevention (or treated if possible). We do adoption events just about every weekend, regularly at a couple of places, and then at as many other places as we can to get our animals before the public as much as possible.
We run 2 resale shops, and do numerous fundraising events as we get no funding from any public or private agency.
No, we can not save every animal, but we do everything humanly possible to save as many as we can. We had about the same number of adoptions last year as a larger nearby shelter with 10 times our budget.
You often hear people talk about no-kill shelters as if they were the only ones that should be supported. I'm very proud of our shelter and what we do for the people and animals in our community. I hope more people come to understand how much we are all doing for the animals in our own way.
I hope the day comes when there are so few unwanted animals that no animal needs to lose its life for lack of a home, but that day depends on people to spay and neuter, and not to take bringing an animal into their home lightly. In the meantime, my open door shelter is giving many animals a chance at a new life they wouldn't have had otherwise.
Thanks for asking, PF!