Hey Tim!
The clay you are referring to is pottery clay. The types of clay that were introduced at the beginning of the learning flow do not need firing in a kiln.
Some dry by simply being exposed to air (WED water-based clay; air-dry clay), others can be baked in a regular oven at about 275 degrees Fahrenheit (Polymer clay), and the others (castilene/Cx5 and all types of oil-based clays) need to be molded in a flexible molding material - such as silicone or latex - to produce a permanent copy of the original clay sculpture in resin or gypsum.
Except for polymer clay and air-dry clay (to a certain extent), none of these materials are suited to yield a permanent sculpture and they will always require mold-making.
I suggest you look through the videos of "Sculpting Mediums" to see each of them in action and get more detailed info on how to handle each material: https://cgcookie.com/course/sculpting-basics/
And if you have further questions down the road, please don't hesitate to ask! :)
~Lisa
