Tatting uses a shuttle to create 'knots' and circles, or tiny picots, and when done over and over can create a beautiful lace that can look similar to a very fine crochet lace piece.
Cro-tat uses a small crochet hook to create the tatting, instead of the usual "shuttle" that tatters normally use.
Tatting is an art, one that you don't hear about as often as knit or crochet. My husband's aunt use to tat constantly, it was her special gift (her hands were always moving and working - constantly) and she made many special gifts for his family, until her death a few years ago when she was in her late 90's.
I would love to learn how to do it, and have noticed that my LYS (local yarn store) does sell shuttles. A few years ago I bought a VHS video on tatting called 'Tatting I - The Basics' by Mildred Clark, brought to you by Victorian Video Productions.
I also bought 'Tatting Beginner Tatting Kit Quick and Easy' (Item number 5050-K) from the Tatsy company, which includes a shuttle with instructions for making an Angel, Photo Frame, Flower, Book Mark, 2 Mini Flowers, 2 Butterflies.
I admit I haven't checked it out yet or haven't delved into the art yet, I have been holding onto it for 'one of these day' (I love needlework, stationary, and art supplies and have probably a lifetime amount of them as I have noticed that many others do as well out there, off my Amazon emails "What do you like to craft" that comes to me, but that is probably another post entirely! It's a SICKNESS! But such a fun one.) but maybe you can still get it on the web or Ebay, if you are interested in learning tatting.