I am not really happy about either of these terms - I believe that both are the result of literal translations in the past, and we all know that the the GDT can be misleading, often giving poor literal translations. Also a google search gives one result (and that's a french article). Certainly we are clear that it is a combination of uncarthrosis and "discarthrosis":
Dorlands medical dictionary gives:
uncarthrosis (un•car•thro•sis) (ungkahr-throsis) bone disease involving the uncinate processes of vertebrae
But has nothing to say about discarthrosis which makes me think it is made up.
Also see link below for terminology discussion (copied here). Unfortunately without reading the whole article I cannot say what they mean to use instead of discoarthrosis:
"OBJECTIVES--To redefine and comment on terms on a pathological basis, in order to avoid the confusion due to the use of terms with different meanings, to standardise usage among clinicians, radiologists and pathologists, and to facilitate literature searches. METHODS--Within the Committee of Pathology of the European League against Rheumatism, a study group was set up to analyse the medical literature and common practice concerning the nomenclature of rheumatic spinal diseases. The group tried to amalgamate the main trends in the field, to reconcile etymology, historical background, morphology, and common practice. RESULTS--The group warns against use of the terms 'acquired hyperostosis syndrome', '(von) Bechterew's disease', 'Kummel's disease', 'pseudospondylolisthesis', 'rheumatoid spondylitis', 'spondylarthropathy' in the sense of spondarthritis, and 'spondylosis'. It recommends intercorporal or interapophyseal rather than intervertebral (osteo) chondrosis, zygapophyseal diverticulum rather than cyst, disc hernia rather than prolapse, spondyloarthritis rather than spondyloarthropathy, marginal rather than anterior spondylitis, and discarthrosis. It proposes 'zygarthrosis' to designate zygapophyseal osteoarthrosis. CONCLUSIONS--Knowledge of the pathological basis of diseases and an understanding of the original definitions given by those who coined new terms make it possible to avoid most of the confusion arising from improper use of spinal terms."

Hope this helps!! But we should all try to avoid using made up terms where possible.