What is a Back Sprain
In your back or neck you have many joints, your disc is actually a joint, and then at each vertebral segment you have 2 other joints called facet joints (in your thoracic spine you also have a rib joint on each side. Around all these facet joints you have small ligaments and when you over-move your back or neck, when you are lifting or fall etc, these little ligaments can be sprained. The material your disc is made from is also the same material and you can also say that you sprained your disc.
In many years of Physiotherapy practice, I have heard lots of people talk about straining their back muscles, but I have never seen an MRI, CT or Ultrasound scan or any research article actually talk about back strains, it is always back sprains or disc injury.
So that is why the most accurate description of an acute back injury is to call it a sprain, it then goes through the same healing processes of any ankle sprain, which is weeks for a minor injury and months for a more severe injury.