All the above are true. In fact, when I first got Kayla, I noticed that her poop was a little soft, with a little mucus. Of course, worrywart that I was, immediately rushed her to the vet
where they took a fecal sample, and pronounced her parasite-free, and said it must be the food. But wormed her anyway.
One month later, poop still soft, still a little mucus, no worms I could see. Indoor only at the time. Back into the vet. Another sample, no parasites. So they alarmed me by saying that she could have all kinds of horrible things, etc. and drew up a $300 testing program to figure out what was wrong. Didn't sound right to me, so I took her home to think about it and do some more research.
One hour back from the vets, Kayla shoves her butt in my face, and there's white thingies wriggling around.
Of course, much reading up on worms, and their life cycles, which are persistent. So depending on the life cycle, it may take a while to rid your cats of them.