A personal relationship is one where your personal life and extra curricular activities and social life are involved.
A work relationship is another way of describing a relationship with your coworker. You spend time together at work, you work well together, but you have little or no contact outside of work. It's strictly professional.
It varies; at first professional relationships are based on getting the job done effectively and without conflict.But over time many colleagues do become friends and will socialise out of work. But they will not let this interfere with their work if they behave professionally. I have friends I have worked with for many years, but at work we just carry out our duties, though we will discuss what we are doing at the weekend and meet up outside of work.
A work relationship to me means getting along with, and enjoying working with, people at work. But that's it... I don't usually talk to them, or 'relate' to them except at work, or work functions.
A personal relationship is one that I enjoy spending time with anywhere I might be... A person who is part of my life.
people must be careful about personal relationships with landlords and tenants