MrEd is an extension of MzScheme for graphical programming. MrEd is described separately in PLT MrEd: Graphical Toolbox Manual.
DrScheme is a development environment for writing MzScheme- and MrEd-based programs. DrScheme provides debugging and project-management facilities, which are not provided by the stand-alone MzScheme application, and a user-friendly interface with special support for using Scheme as a pedagogical tool. DrScheme is described in PLT DrScheme: Development Environment Manual.
The mzc compiler takes MzScheme (or MrEd) source code and produces either platform-independent byte code compiled files (.zo files) or platform-specific native code libraries (.so or .dll files) to be loaded into MzScheme (or MrEd). The mzc compiler is described in PLT mzc: MzScheme Compiler Manual.