A Concept map is similar to a Mind-map, however a mind map often works on the assumption that there is a single central node and a tree structure down from there. Some more advanced mind-mapping software has the ability to draw a link between two nodes on different branches, however this is more of an add-on to show relationships between the two concepts, rather than an equally important branch.
Concept Mapping software allows these more complex concept maps to be captured and shared, including loops, decision trees and process maps.
Inspiration was originally designed for use in schools as an alternative to traditional outlining. It is true concept-mapping, in that you don't have to have a single central node. Also, the connectors can be labelled as well as the nodes. Costs around $70.
CMAP seems to be a favourite, however some have issues with some of the features. It is a full business product and so costs around US$199.
Mind mapping is covered fairly comprehensively at these site: