As I read it, the wikipedia article states the CBF is square. The rectangular flag is the Confederate Navy Jack.
The rectangular flag was used by the Confederate Navy as you say, but also by the Southeastern Department (flown by state troops serving at home), by the Army of Tennessee, and by units in the Trans-Mississippi Department like the one preserved by its color-bearer after Jo Shelby took his command into Mexican exile rather than surrender. (He sank his colors in the Rio Grande, but one color-bearer went back and retrieved his. It survived and is now a vexillological document, and -- like most Texas Confederate flags -- an unsurrendered Confederate color.)
The original Army of Tennessee flag had 12 or 13 large, six-pointed stars (because the officer appointed to see to it knew his European heraldry conventions) and was 1:2 oblong, later shortened to "about" 4:6, 3:5, and similar proportions, and given five-pointed stars. This flag, with 13 stars, is the one we know today as "the Confederate Battle Flag".
Lee's Army of Northern Virginia carried a square flag with 12 stars, the stars being bunched slightly toward the crux of the saltire and the ends of the arms left unadorned.
In the West generally, the flag was almost always oblong, but the colors of the flag were sometimes shown reversed, with no white fimbration to the saltire/St. Andrew's Cross; this was the rule in Taylor's Corps, which served in the Trans-Mississippi Department. Polk's Corps, until the last year of the war, flew a blue battle flag, sky-blue at first and dark blue later, with a red St. George's Cross (Polk was an Episcopal bishop before the war). The flag's cross was at first without fimbration and decorated with 13 large, five-pointed stars and so carried in 1861-2. The stars were slightly smaller and reduced to 11 on the later dark-blue version carried in 1863-4 (two stars being deleted from the vertical arms to regularize the spacing), and a white fimbration was also added to the cross; the whole effect was a little like an Icelandic flag with equal arms and white stars on the arms. I'd like to have one of those flags myself, but they're rare and available only from (understandably expensive) re-enactment outfitters.