Craft woodburners are intended as the name implies, for CRAFTS. They are not intended for detail work. These are used by Crafters who are not looking to do fine art but, simple projects such as signs, projects for kids and so forth. These woodburners take ALOT longer to heat up and cool down.
Craft woodburners are one piece and plug right into the wall. The hand pieces are large and awkward. These are not comfortable if you intend to woodburn for long periods of time.
The nibs are screwed into the burner and the burner must be COLD so you do not get burned or run the risk of stripping the threads which are very fine and made of Brass.
Variable Temperature Detail burners (ie: Colwood & Razortip to name two) are designed for an Artist who wants to do fine detail work on wood, leather, gourds etc.. Typically these are used by Artist wanting more detail work incorporated in their design/project.
These burners come with a power source and separate hand pieces that attach the power unit with a cord. The hand pieces are smaller in diameter than the Craft burners which makes it more comfortable for long periods of woodburning. Grips such as cork or foam make it even more comfortable to use. They are cooler on the hand and some brands come with vented hand pieces. Some brands offer fixed tips and interchangeable tips. The fixed hand pieces are sturdier and give you better heat flow.
It really all boils down to the preference of the Artist.