Categories…Mine and Yours

Hi!
Quick multi-part question about categories 🙂 Is there a global, WordPress-wide category search? If so, where can someone search for them?

I’m asking because I read a WordPress tip post that said categories are linked. If someone searches for “kittens” they’ll see every WordPress blog post tagged with a kitten category. If I have a “cute kitten” category, my post won’t show up. is such the case? If so, I’ll go back and re-name and re-categorize.

Most of my categories and tags were ported over from my old Blogger blog. I want to fit in here as best as I can 🙂

Are there any helpful hints or ideas with this request?
Many thanks,
Scott