The main characteristic of globular and fibrous proteins is their structure. Globular proteins are "spherical" (or globular) in structure and function mainly as metabolic proteins. They are generally soluble because of the dipole-dipole interactions happening in the structure.
Fibrous on the other hand are long, thin and rod-like in shape which is essentially for structural and support purposes. These proteins form our connective tissues, tendons, bone matrices and the muscle fibres. They are generally insoluble types of proteins.
Fibrous and globular proteins have primary and secondary structures but only globular proteins have tertiary and quaternary structures.