Memorial Day is the commemoration of military service that grew out of the Civil War. Today is the one that grew out of the end of World War I, or First World War as the British refer to it.
Nonetheless, both commemorate the service of all veterans and that includes the Civil War veterans. And, even though some people hate this idea, those who served the Confederacy are also included as our nation's veterans.
So, To All Veterans, a Very Big Thank You