We use the terms upper case to describe capitalised letters and lower case for small letters. But the nomenclature does not come from the computing paradigm.
When books began being written, books were handwritten, or rather hand-copied. Since books were written on leather, leaf or papyrus, they had limited shelf life and often had to be copied over and over as the document aged, to preserve it. Writing books by hand was expensive because it was so time-consuming. Every letter had to be written legibly so that anyone would be able to read it.
This resulted in the advent of cursive writing in ancient Rome and Greece. The word Cursive is derived from the Latin word ‘Cursivus’ which means running. Running handwriting sped up the process of writing while at the same time preserving the legibility for all readers.
With the advent of printing, there was a need to replicate the beauty of cursive writing while printing books. Every letter had to have a capitalised and a small form. Two forms of every letter were created, and they also needed to be stored separately so as not to confuse the two.

The terms "upper case" and "lower case" have quite literal meanings. Printers stored the capitalised letter in the upper part of a case, and small letters were stored in the lower case. This carried forth from the printing world into computing, and thus we call capitalised letters upper case and small letters lower case.