Question: Did the Battle of Chickamauga and Operation Nordwind occur in different wars?

Context articles: Operation Zahnarzt
Fortified Sector of Rohrbach
Herrlisheim
Battle of Chickamauga
List of Canadian military victories
Ouvrage Simserhof
Colmar Pocket
Order of battle for Operation Nordwind
827th Tank Destroyer Battalion
Operation Nordwind

Operation Zahnarzt (literally "Dentist") was a plan by the Germans to eliminate the Third Army during World War II.
 The plan of Operation Zahnarzt was to immediately come after Operation Nordwind.
 The plan was to initiate a pincer movement to encircle and destroy the 3rd US Army.
The Fortified Sector of Rohrbach ("Secteur Fortifié de Rohrbach") was the French military organization that in 1940 controlled the section of the Maginot Line in the vicinity of Bitche.
 The sector was bordered to the west by the Fortified Sector of the Sarre and to the east by the Fortified Sector of the Vosges.
 With lower priority than other sectors, the SF Rohrbach was built somewhat later than its neighbors to the east and west, and in company with positions on the extreme western end of the Maginot Line, became one of the "New Fronts."
 The sector contains several major "ouvrages" and was the scene of fighting in both 1940 and 1944.
 It was attacked in 1940 by German forces in the Battle of France.
 The sector was heavily engaged by German forces in mid-June 1940, with several casemates and the "petit ouvrage" Welschhof surrendering before the Second Armistice at Compiègne.
 The remaining positions and their garrisons finally surrendered on 27 June 1940.
 In 1944 German forces occupied several positions in the SF Rohrbach, forcing advancing American forces to attack them individually or to bypass them.
 The German Operation Nordwind offensive of early 1945 caused American forces to fall back, returning to complete the capture of the Rohrbach sector in March 1945.
 Following the war many positions were reactivated for use during the Cold War.
 Two locations are now preserved and open to the public.
Herrlisheim is a commune in the Bas-Rhin department in Grand Est in north-eastern France.
 The town dates from the 8th century.
 Herrlisheim was the scene of very heavy fighting during "Operation Nordwind", an offensive launched by the German Army during World War II that inflicted considerable damage to the town.
The Battle of Chickamauga, fought on September 18–20, 1863 between Union and Confederate forces in the American Civil War, marked the end of a Union offensive in southeastern Tennessee and northwestern Georgia — the Chickamauga Campaign.
 It was the first major battle of the war fought in Georgia, the most significant Union defeat in the Western Theater, and involved the second-highest number of casualties after the Battle of Gettysburg.
The following are battle victories by Canadians in different wars.
 According to the below list, Canadian victories are French victories prior to the British Conquest of Quebec (1759).
 Prior to this conquest, any victories by the British in Nova Scotia (even after the Conquest of Acadia in 1710) and aboriginal victories over the colonial empires are not considered Canadian victories (e.g., see aboriginal victories in Father Le Loutre's War).
Ouvrage Simserhof is a "gros ouvrage" of the Maginot Line, located near the community of Sierstal in the French "département" of Moselle.
 Simserhof is adjoined by "petit ouvrage" Rohrbach and "gros ouvrage" Schiesseck, and faces the German frontier.
 Located 4 km to the west of Bitche, the "ouvrage" derived its name from a nearby farm.
 It was a part of the Fortified Sector of Rohrbach.
 During the Battle of France in 1940, Simserhof supported its neighboring fortifications with covering artillery fire, with partial success.
 After the surrender of France, it was occupied by the Germans as a storage depot for torpedoes, and later resisted the American advances of late 1944.
 Taken by the Americans, it was briefly re-occupied by the Germans during Operation Nordwind.
 Following the war it was repaired for use by the French Army, but was proposed as a museum of the Maginot Line as early as the 1960s.
 Retained by the Ministry of Defense, Simserhof now functions as a museum, and has the most extensive visitor infrastructure of any of the preserved Maginot fortifications.
The Colmar Pocket (French: "Poche de Colmar" ; German: "Brückenkopf Elsaß" ) was the area held in central Alsace, France, by the German Nineteenth Army from November 1944 to February 1945, against the U.S. 6th Army Group during World War II.
 It was formed when 6th AG liberated southern and northern Alsace and adjacent eastern Lorraine, but could not clear central Alsace.
 During Operation Nordwind in December 1944, the 19th Army attacked north out of the Pocket in support of other German forces attacking south from the Saar into northern Alsace.
 In late January and early February 1945, the French First Army (reinforced by the U.S. XXI Corps) cleared the Pocket of German forces.
This is the order of battle of German and Allied forces during Operation Nordwind in World War II
The 827th Tank Destroyer Battalion was a tank destroyer battalion of the United States Army active during the Second World War.
 It was activated in April 1942 as a segregated African American unit, deploying to Europe at the end of 1944 and attached to 12th Armored Division.
 It saw action during Operation Nordwind in January 1945, where elements of the battalion performed creditably.
 However, its overall combat record was marred by severe disciplinary problems and insufficient training.
 It was withdrawn in February, and assigned to rear-area duties; while it nominally remained active for the remainder of the war, it had been effectively disbanded.
Operation North Wind (German: "Unternehmen Nordwind" ) was the last major German offensive of World War II on the Western Front.
 It began on 31 December 1944 in Alsace and Lorraine in northeastern France, and ended on 25 January.