Q. How do I classify the type of plant that I am propagating?

A. There are three categories of cuttings: softwood or succulent, semi-hardwood (greenwood) and hardwood. There is some cross over in the categories, but usually they are easy to identify.

a) Softwood/Succulents: The emerging growth of most plants are classified as softwood. Things to look for are cuttings that can be easily bruised with a nail, cuttings that can be  easily broken and cuttings that wilt rapidly. To avoid wilting, softwood or succulent cuttings should be kept cool and moist. Very softwood cuttings may rot.(1)
b) Semi-hardwood: May be applied to broadleaf evergreens when the wood is firm and leaves have matured.(1)
c) Hardwood: Deciduous plants after they have lost their leaves in fall, needle evergreens and broadleaf evergreens. Cuttings for needle evergreens are usually rooted under greenhouse conditions.(1)

References:
(1) Dirr, Michael and Heuser, Charles. The Reference Manual Of Woody Plant Propagation. Athens, GA: Varsity Press, 1987.