The .45 Colt (often called .45 Long Colt) is primarily a revolver cartridge while the .45 ACP (often called .45 Automatic or .45 Auto) is primarily a semi-automatic cartridge.
The .45 Colt was originally introduced in the Colt Model 1873 Single Action Army revolver. It was originally loaded with black powder and thusly is a much larger case than the .45 ACP. Over the years, this cartridge has been chambered in a wide variety of single and double action revolvers as well as carbines of differing action types. To my knowledge, there has never been a semi-automatic handgun chambered for .45 Colt. Standard ballistics are a 250-260grn bullet at 800-900fps although in certain guns like Ruger revolvers, Freedom Arms revolvers, and Thompson Center Single shot handguns and rifles it can be safely loaded power levels roughly equal to a .44 Magnum (note that not all .45 Colt firearms are safe to do this in).
The .45 ACP was devised by John Browning and was chambered for a number of prototype handguns but the first to achieve widespread manufacture in this caliber was the Colt M1911 semi-automatic pistol. The .45 ACP was designed to give approximately the same ballistics as the .45 Colt handguns then in use in a semi-automatic platform and it does this farly well with standard loadings delivering a 230grn bullet at 800-900fps. Because of the development of smokeless powder, the .45 ACP case was made substantially shorter than that of the .45 Colt (it takes much less smokeless powder to give the same velocity than it does black powder). Also, because semi-automatics headspace and extract differently than revolvers, the .45 ACP is a rimless case (there actually is a rim, but it's the same diameter as the rest of the case as opposed to the .45 Colt and most other revolver cartridges whose rims are larger in diameter than the rest of the case to ensure proper headspacing and extraction). The .45 ACP has been chambered for semi-automatic pistols and carbines as well as some revolvers. In double-action revolvers such as the Colt and S&W M1917's, the .45 ACP is typically used in conjuction with a moonclip which holds multiple rounds and provides a surface for the extractor to work against. In single action revolvers such as the Ruger Blackhawk, a lip is machined into the cylinder that allows the case to headspace on the cartridge mouth similar to headspacing in a semi-automatic chamber (extracion is accomplished with an extractor rod just like any other single-action revolver). Single action revolvers chambered for .45 ACP are often provided with two interchangeable cylinders thusly allowing either .45ACP or .45 Colt ammunition to be fired depending upon which cylinder is installed.
As far as how the .45 ACP stacks up as a self-defense cartridge, that is a topic of great debate (as you'll soon learn if you stick around here long). Few would argue that the .45 ACP is an excellent self-defense cartridge (it has been standard issue for many militaries and police forces including the U.S. military from 1911 until 1985 when it was replaced by the 9mm), but the debate lies in how much better, if any, it is than other common self-defense cartridges such as 9mm, .40 S&W, .357 Sig, and .38 Special. Personally, I think that with proper shot placement and premium JHP ammunition, the difference between the service class of cartridges (.45 ACP, .40 S&W, .357 Sig, 9mm, and .38 Special +P) is negligable and the results are likely to be nearly identical. Only in smaller cartridges like .380 ACP, .32 ACP and .22 Long Rifle or in Magnum class cartridges like .357 Magnum, certain 10mm Auto Loadings, .41 Magnum and .44 Magnum are you likely to see a noticable difference in terminal performance. The .45 Colt's terminal performance is subject to what type of loading is used, in standard loadings it will be very similar to .45 ACP and in heavy loadings for strong guns like those I previously mentioned it will be more similar to the .44 Magnum.
As a hunting handgun, the .45 ACP is pretty marginal for deer-sized game and completely inadequate for larger game like Bear or Moose. The .45 Colt on the other hand can make a splendid hunting handgun with the right loadings from the right gun. A 250grn+ bullet at 1000fps or more makes an excellent deer cartridge and with the heavier loads it is capable to taking about anything that a .44 Magnum can.
A Taurus Judge would not be a good handgun for big game hunting as the long cylinder is detrimental to accuracy with .45 Colt ammunition. Many of the reports I've read report keyholing (this is where the bullet destabilizes and begins to tumble end-over-end) at 25 yards with .45 Colt ammo. In addition to this, the Judge is not able to handle the pressure of .44 Magnum-Level loadings that other stronger revolver can. As a self-defense gun, a .45 Colt-loaded Judge would be acceptable though no better than any other so-chambered DA revolver. The main advantage to the Judge is the ability to use .410 Shotgun shells (it is listed as chambered in .45 Colt to avoid the stringent regulations on shotguns with barrels shorter than 18 inches). While the use of .410 Shells for self-defense is debatable (low pellet count with buckshot, poor accuracy and shallow penetration with slugs, and shallow penetration with birdshot), a Judge loaded with birdshot would be useful for short-range hunting of small game like rabbits and squirrels and for elimination of pests such as rats and venomous snakes.
