Worms?!

So a couple months ago I noticed white mucusy stuff on the rear of my cat.  I did some research and assumed it was just mucus.  I assumed he was fine because we had just taken him to the vet for his kitten check up since we had just gotten him.  I thought they would have told us if he had worms or something.  But just the other day I noticed he still has the mucusy stuff on his rear, and so I started researching it and i'm scared its tape worms!  It kind of looks like rice on his rear which is how webmd defines it.  And it almost looks like it is moving but I can't tell if it is just because my cat is moving.  But he has no health issues.  I mean his poops are stinky but look fine, and he seems fine.  I'm planning on taking him to the vet as soon as possible (although it's christmas today).  

Does what I describe sound like tape worms? Can my family catch it?  And is he gonna be ok--it's been several months that he has had it I think.  Also my other cat shows no signs of this, but is he likely to get it?  

Tapeworms are the results of ingested fleas, so make sure you get him to the vet for a flea treatment (NEVER use anything over the counter as that can be fatal) and also for a tapeworm treatment.  Tapeworms are very common, especially if you've noticed fleas.  They need a special medication because they're not killed with the normal dewormer.  You can't catch them.  As for the mucous, that might have something to do with his anal glands.

Tapeworms caused by fleas is just one type of tapeworm. They can also come from eating rodents. Does your boy have a history of going outside? That could explain why he has it and not the other cat. You can check through his fur to look for dirt as it could be flea dirt indicating fleas. More than likely he will need to see a vet for treatment. As long as he is healthy and acting normally otherwise you can take some time to save up for that as it's not an emergency. However now that you know of the problem you really shouldn't let it go on too much longer. As far as your family catching it, you would have to ingest the white pieces from his bottom in order to be infected. Or if it's caused by fleas you would have to ingest the fleas.