We need an 'intro to cattle' sticky so we can lay some groundwork as far as industry specific terminology is concerned.
Stabilized composite breeds are those such as beefmaster, brangus, santa Gertrudis, etc. While derived from crossing more than one purebred lines, these stabilized composites are now considered to be purebreeds of their own as a result of their now STABILIZED GENOTYPE. Example: ALL Brangus are 5/8 Angus 3/8 Brahman. Note that this is much different than just a random combination of angus and Brahman blood. It is a specific genetic makeup that was stabilized, i.e. FIXED, by breeding 5/8- 3/8 animals to each other for multiple generations.
Just because the pedigree or lineage of an animal has been documented has no bearing on an individual's purebred, crossbred, or mongrel status.
A purebred is an animal with a stabilized genotype: Angus, Hereford, Santa Gertrudis, etc. These pure lines are also known as seedstock.
A crossbred, or f1, is the result of crossing two stabilized purebreds of different breeds: Black baldie, Balancer, f1 Durham Red, etc
A mongrel, is an animal whose genetics are in disarray as a result of multiple (more than 1) outcrosses: Stabilizers (misnomer, I know), random multicross cow in your neighbor's pasture, etc