For twins, zygosity refers to the degree of genetic similarity within each pair.
There are two different types of twins:
Dizygotic (DZ, fraternal) twins occur when two eggs are released at a single ovulation and are fertilised by two different sperm. These two fertilised eggs then implant independently in the uterus. DZ twins share around 50% of their genes which is the same type of genetic relationship as non-twin siblings, hence the term fraternal , and:
Monozygotic (MZ, identical) twins develop when one egg is fertilised by a single sperm and during the first two weeks after conception, the developing embryo splits into two. As a result, two, genetically identical babies develop.
A zygosity diagram can be downloaded here
A publication by the TRA team discussing why it zygosity determination is important for twins and science - and how the accuracy can be improved, can be downloaded here