AddMusic is the name of a series of tools created for the purpose of inserting custom music to Super Mario World. The original AddMusic was created by Carol in 2007. It was discovered by the English-speaking community on 28 June 2007 when mikeyk posted a thread about it on Board 2. Since then, many alternative versions of the program have been made by other hackers to make it more versatile and compatible with real SNES hardware.
AddMusicE, also known as Addmusic_e or Carol's AddMusic, was the original AddMusic tool. It was created by Carol in early 2007, though the exact date is unknown. It originally only had support for adding music to SMW's overworld, but support for level music was implemented several months later. It was developed in Perl, but requires the user to have Java installed to run properly.
The second AddMusic, and for a while the most popular version. Created by Romi.
AddMusicM, or AMM, was created by homing and 757, and released on 15 January 2010. It was built separately from the previous versions, and contained many new features, including new N-SPC commands and allows the usage of .BRR samples. It requires ActivePerl to run properly. Once the early versions were released, it quickly became widely used despite still having been considered incomplete by its creators.
AddMusic4.05, known as AM4 for short, was created by HuFlungDu as an alternative to AddMusicM while AMM was still in development. It was first publicly announced on 19 February 2011. It was based on Romi's AddMusic (version 4.04 specifically, hence the name), and is functionally very similar. Although it lacks many of the features that made AddMusicM so desirable to many people, it was much more stable than AMM's WIP incarnations and became widely used in its own right. Even though the tool was only ever meant to be temporary, it led to a long-lasting debate between people who preferred either AMM or AM4, a debate which didn't end until the release of AddMusicK.
AddMusicK, or AMK, was created by Kipernal in 2012. It was first announced with a beta release on 7 October 2012, and its first official release was on 31 December 2012. In theory, it's as stable as AM4 while containing all of AMM's special commands and features, making it the best of both worlds. As such, it has since been considered the standard tool for inserting music into SMW, and all ports in SMW Central's music sections are required to be compatible with AMK to be accepted.