That is almost right Greg...cacti have spines. But there are other succulents with spines, that are not cacti.
I found this page: gives some info on how to differentiate another type of spiny succulent from a typical cacti:
http://www.weekendgardener.net...
But to keep it simple for me...with spine could be cacti....succulents in general would be any plant that holds/hoards water either in its leaves, in its stems/caudex, or in its roots.