No. The .450-400 Nitro is a .450 case necked down to shoot a .410," 400gr bullet at 2,150 f/s (with a 300gr load also available). The .450 Nitro is a true .45 caliber--bullet diameter being .458," and throwing a 480gr slug also at 2,150 f/s. They both evolved from former black powder cartridges, and the older of the two is the 1898-vintage .450 NE, a Rigby brainchild. The .450-400 NE was introduced by Jeffery in 1902, and quickly became the standard all-around African cartridge, only to be supplanted by the .375 H&H in 1912.
Another issue that worked against the otherwise-excellent .450 Nitro is that the British banned it in India and the Sudan IIRC in 1905, to prevent uppity locals from reusing bullets from the old British military standard .577-450 Martini-Henry round. Hence the introduction of cartridges like the .465, .475 and .476 around 1907-1910. Probably not something you needed to know, but an interesting piece of trivia nonetheless.