Yes Mick, they are different cases, and what you end up with is acentually a wildcat, that is formed by fireing a slightly shortened, factory Flanged case in the H&H chamber that has had the belt area is removed,bushed, and re-cut. Sort of like a 375 Flanged improved! Still you have a flanged cartridge instead of a belted rimless one, and ballistics are about the same. Here are the numbers, in inches!

375 Flanged/ 375 H&H Mag

case length 2.94 ............ 2.850

head dia .511 ............ .513

Rim dia .572 ............ .532

neck dia .404 ............ .405

neck length .444 ............ .300

shoulder Lgth .096 ............ .197

body angle .794 ............ .705

loaded length 3.08 ............ 3.60

belt dia N/A ............ .532

rim thick .05 ............ .o49

shoulder angle 13.47 .......... 7.95

Shoulder dia .450 .......... .460

case capacity 97.21 .......... 96.37 grs water

The 450 NE 3.25" or the 450#2 either will completely clean out the 458 Win Mag chamber, so it is a no brainer, but sometimes needs re-regulateing! Most times they don't, because they push their bullets at about the same speed.