We have indoor kitties who love to sit and loll in the windows and look outside enjoy the redneck tv we have for them [bird feeders] and just love feasting and sitting for most of the day…like most cats I’d assume.
Every night for the last several nights we have had a visitor to our back window…a smallish raccoon. He eats his fill of bird seed that has fallen from the feeders and leaves. The cats rush over to that window and look at him for a little while then they hunker down and do nothing…just close their eyes and loll in the evening wind coming from the window.
Ok now insert a cat in the same scenerio: Cat walks up to the house and decides to chill under a window. Our cats go bizerk! They hiss and spit and spat untill the outdoor feline goes away…Why the species differential? Why don’t they get angry at the raccoon, but pissed to all hell at the cats?
They know the raccoon is not another cat, he’s potential prey* and is interesting to watch and they don’t want to alert him to their presence. Other cats are interlopers into their territory and are not welcome and are told such by the hissing.
*obviously they’ve never really met a full-grown raccoon up close and personal or they wouldn’t think this.
I think Wile E has it, but you could always go with the answer we use in our house whenever we can’t explain a strange cat behavior – it’s because his brain is the size of a walnut. 
I should have just used my standard “cats are weird” answer. It always works.
I agree with Wile E in both instances. We’ve two indoor cats. Neighbors have dogs out all night, lots of squirrels, & we’ve two skunk “neighbors” living very nearby. No response from either cat. BUT–one outdoor cat, especially a tom, in the yard, then it’s hissing, spitting, trying to claw through the window, etc.
Yup, Wile E, cats are wierd.
I have one indoor cat who does spend time on our screened porch.
We have had both outdoor cats as well as racoons visit.
She hisses at both through the screen, and they reluctantly retreat.
In my experience around here where we have lots of 'coons and possums, cats don’t react to either. Obviously cats can tell cat from non-cat, and I guess certain animals are big enough to not register as prey, but small enough to not register as predator.
My cat would sit in the same tree with the raccoons, just hanging out. I could dangle a baby possum right in front of his face and he’d politely pretend not to notice.
Cats are weird.
Having been woken up on Thursday night by a fight between a raccoon and a neighborhood stay cat, I say your experience is not universal. Our cats hate the raccoons, too.