A personal relationship is formed by choice and it is generally with someone you share the same interests with and who you like. You are able to discuss personal opinions with one another. Personal relationships can include intimate romantic relationships-this is unacceptable in a workplace relationship due to professional boundaries.
A working relationship is where you are placed in a work place with other people and work as part of a team. You do not have to like the people you work with however it is important your personal feelings and opinions towards colleagues are kept to yourself. Within a work place relationship there are professional boundaries and policies with much be adhered to, whereas within a personal relationship there aren’t any restrictions.