According to Purdue University's Online Writing Lab, personal correspondence is defined as either personal letters or newsletters. Personal letters include many sorts of communication, from holiday salutations to letters of complaint. Newsletters are intended to inform readers on a subject.
Compared to emails, personal correspondence is intended to give the reader a feeling of closer connection to the writer. Because personal letters take greater time and effort to write and send, they may carry more weight and be read with more care. This can create a variety of effects: a personal letter of complaint can serve to emphasize the level of disappointment, while a personal holiday letter can serve to emphasize the connection between the sender and their readers.