The terminology is very misleading, because SEMI-UNCIAL is not half of the Uncial script; moreover, the comparison between the two scriptures is also improper, because there is no genetic relationship between them. It is true that there are some similarities, but these depend on the fact that both are indebted (at least in part) to primitive minuscule writing, the first Minuscule that was also used for books in the 3rd century.
The origins of the semi-uncial script
After a first phase of slow formation that began from the 3rd century, which paleographers indicate as “primitive” or “rustic” semi-Uncial, the new semi-Uncial script acquired definite and particular characteristics starting from the 5th century. At this time the production of books in Minuscule, which was confined (with few exceptions) to a scholastic or private level, began to take place in actual centers of writing, particularly in the ecclesiastic ones, perhaps in Africa. It is a specialized type of Book Minuscule, with letters that tend to have a round shape. It was called semi-Uncial by the Maurini, Charles François Toustain and René Prosper Tassin of the Nouveau traité de diplomatique (vol. III, Paris 1757, p. 204 sgg.) who considered it a Minuscule that derived from Uncial, but the term is ambivalent. The medieval expressions used to indicate this writing are “litterae Africanae” or “litterae tunsae” (from tundo: beaten, struck). Up until the end of the 19th century, it was believed to have derived from the Uncial script. Then, Maurice Prou (Manuel de paleographie, p. 22), and later, Franz Steffens (Lateinische Paläographie, tav. 20) disavowed every link between them and proved that the semi-Uncial script is a calligraphic version of Cursive Minuscule.
In fact, it comes from primitive Minuscule and from New Cursive Minuscule.
Vat. lat. 1322, f. 160v