Does my cat have a tapeworm?

So, my cat was treated for tapeworms a few months ago, but either they treated her for the wrong worm or she is re-infected. I saw a very thin, white worm (or segment or whatever it is) coming out of her anus today. I looked where she sleeps and found the whitish brown rice-grain looking things I found before are back too. I'm just confused because from what I understand the "segments" that come out of the anus are supposed to be small and maggot-like, but these are thin and are still wriggling around. ???.