What is the difference between these versions of the KJV? I found those versions of the King James Version:


King James Version (1769) including Apocrypha
King James Version: Pure Cambridge Edition
American King James Version


Is there any difference between them?
The American King James Version seems to be a fairly new revision of the King James to update the spelling and vocabulary of the KJV to match modern usage and remove archaisms. In that sense, it's similar to the more popular NKJV (New King James Version). The AKJV looks to be the hobby project of a single person of unknown qualifications, so it's reliability is questionable.

(source: http://www.crosswire.org/sword/modules/ModInfo.jsp?modName=AKJV)

The other two are far less substantial revisions of the original 1611 text, mainly fixing spelling, grammar, and glaring errors. Virtually nobody uses the 1611 text anymore, most KJV bibles you find are using one of the later editions. The 1769 version you have there is the Benjamin Blayney's edition, which was the standard text for quite some time. In 1873 the Cambridge Paragraph Bible came out, edited by F. H. A. Scrivener. Scrivener reformatted the text into paragraphs (and formatted poetry to look like poetry), and he meticulously corrected errors in the text and noted changes from the 1611 version in an appendix. Unlike Blayney, Scrivener made changes that affected the meaning of the text when he thought the original translators were in error.

It seems that most KJVs published today are based on the 1900 Pure Cambridge edition, but I can't find much information about its origins. Most sources online are from KJV-only apologist websites, which are about as far from reliable sources as they come.

Sources:

http://www.crosswire.org/sword/modules/ModInfo.jsp?modName=AKJV

https://bible.org/article/changes-kjv-1611-illustration

http://www.cambridge.org/us/academic/subjects/religion/biblical-studies-new-testament/textual-history-king-james-bible-and-new-cambridge-paragraph-bible

http://www.cambridge.org/us/academic/subjects/religion/biblical-studies-new-testament/king-james-bible-short-history-tyndale-today