The Celestial Union was a planetary alliance in a parallel universe. Bajor was at its center and Earth, Cardassia and many other planets were members.
Starfleet and the Bajoran Militia once existed in the Union's universe and had been amalgamated by the 2370s. Its defense force uniforms were an amalgamation of the two forces uniforms.
The Union was once at war with the Tholians and it was during this conflict that Colonel Benjamin Sisko discovered the Bajoran wormhole. (DS9 novel: Fearful Symmetry)