I have a sway back; is that the same as scoliosis?

It is different. Both are disorders of the spinal column. Scoliosis is a sideways curvature (sidebending or sometimes called lateral flexion) of the spine or a portion of the spine whereas sway back is a backwards bending (extension) of the spine. Usually plain x-rays are done for the initial diagnosis. Treatment consists of special exercises, spinal manipulation and when severe, surgery may be required.
No . A layman's term, a sway of the back is the way the lower back is curved in called lordosis. Generally, this term sway means an increase in this curve. It can be associated with a scoliosis as the typical or idiopathic scoliosis is a 3 dimenstional deformity of the spine which not only gives the side to side curve seen but can affect how round the upper back appears or how swayed the low back is.