Being a 100% Service-connected P&T veteran, and an SSDI Medically Improvement Not Expected (MINE), I can say that although the VA and Social Security are two separate Governmental agencies, they acknowledge one another.
The VA give greater credence to a determination of disability by the Social Security Administration (SSA), that the SSA does for the VA.
There have been many attempts to have benefits for 100% service-connected P&T veterans get SSDI benefits automatically, but the SSA has steadfastly refused and battled for its autonomy using 20 CFR 404.1504 "A determination of disability made by another non-Governmental or Governmental agency is not binding upon the Social Security Administartion..."