Chapter 2: How does zsh differ from...?
As has already been mentioned, zsh is most similar to ksh, while many of the additions are to please csh users. Here are some more detailed notes. See also the article 'UNIX shell differences and how to change your shell' posted frequently to the USENET group comp.unix.shell.
2.1: Differences from sh and ksh
Most features of ksh (and hence also of sh) are implemented in zsh; problems can arise because the implementation is slightly different. Note also that not all ksh's are the same either. I have based this on the 11/16/88f version of ksh; differences from ksh93 will be more substantial.
As a summary of the status: