A General Desire can be defined like this:
A Desire that is shared by most members of a community such as the desire for freedom or love. It is a core desire that we can’t decide not to have. If we are a human being, we inherently have this desire.
A Specific Desire can be defined like this:
A Desire to develop a loving relationship with a specific person. The MC in our story may be attracted to another character and so desire to get to know him better. This is a more Specific Desire than the more General Desire to find and develop a loving relationship.