Glenn Miller formed The Glenn Miller Orchestra in 1937. Later it was disbanded and a second Glenn Miller Orchestra was formed in March 1938, which was disbanded in September 1944. A couple of months after that Glenn Miller disappeared, never to be seen again.
In 1946 the Miller estate authorized a Glenn Miller 'ghost band' under Tex Beneke, and then in 1950 the estate and Beneke parted ways. Finally, in 1956, the Miller estate formed a Glenn Miller Orchestra under Ray McKinley, and that orchestra still exists (after changing bandleader several times).
Here all of these are seen as incarnations of the same orchestra. When Glenn Miller was still alive the orchestra usually performed as "Glenn Miller and His Orchestra".