The new Latin also known as "neo Latin" evolved from the old latin. It is the more eloquent and polished version of Latin. New Latin is the latin spoken by most people. Old Latin was native to Italy and other Latin speaking countries.
Over time, there were changes made in Latin which made it easy for non native speakers to learn, this brought about some changes in the language. New Latin also describes the use of the Latin language for any purpose such as scientific and literary. In its early days, new Latin was used by Catholics and protestants in Europe.
One major difference between New Latin and Old Latin is the evolution of the language. As with any language that has been around for thousands of years, words and pronunciations have changed. Old Latin was a language that usually stayed in and around its native area such as Italy and Greece. New Latin is one that has been catered and customized so it is more widely accepted throughout the world.
The elocution of the language has changed as well with New Latin. New Latin also is the language that is most associated with books written from the modern time period of the 14th century right on up to the 20th century. The obvious difference between Old Latin and New Latin is the language has changed and it has changed to the point where it can be easily adapted and spoken by more people all around the world. It has changed tremendously over the course of time as do most languages that have been around as long as Latin has.