No, they are not. Both have important roles in a therapeutic setting. This can be confusing because some people call a dog that works every day at a facility a therapy dog.
A Facility Dog is specially trained to work at a facility every day and has specific tasks that they do. They go to work (and sometimes live full-time at the facility) every day just like any other employee.
A Therapy Dog is a well-behaved pet, often certified by the Delta Society, Therapy Dogs International or a local therapy dog program. They visit a facility with their owner for an hour or two at a time to give love and affection to the residents or patients there.