You have described well.
Pain is radiating from the buttock to thigh & below.
It’s called radiculopathy
In our back we have vertebral
In between 2 vertebra cartilage
disc is there.
Disc problem cause pain as it irritates the spinal nerves.
is not related to it.
You should have x-ray of lumbosacral region ap & lateral view under a orthopaedic doctor.
Wish you good health.