The simple answer is "No", they aren't the same. .45 Long Colt is a traditional pistol cartridge, as shot from the old Colt .45 cowboy revolvers. They also show up, in single-shot rifles, in "Traditional Hunter" models. Some folks like the idea of having several guns (handgun and rifle) that can use the same round; and it's popular in "Cowboy Action Shooting" (usually with lever action rifles).
The .45-70, -90, etc. are big (long) rifle cartridges ... real heavy hitters, suitable for elk, bear, etc. A .45-70 (etc.) won't fit in a 45LC gun; and, if it somehow did, it would blow it up. The Long Colt is probably OK for deer, at relatively short ranges (maybe out to 125 yards), iffy for boar. Some folks say you can't be "over-gunned" when going after boar, especially the bigger European varieties. Check in with the Wild Boar Hunting forum, elsewhere on Greybeard. You'll see a lot of discussion about what's appropriate ... and what's not. Also, poke around the various ammo manufacturers' sites; you may find some pic's showing the relative sizes (and ballistics).