Versions

REDUCE is based on a dialect of Lisp called Standard Lisp, and the main differences between versions of REDUCE are the result of different implementations of Standard Lisp; in each case the source code for REDUCE itself remains essentially the same. The binary distributions of REDUCE available from SourceForge are based on two different implementations of Standard Lisp, namely PSL and CSL:

Portable Standard Lisp (PSL)
PSL was the original implementation of Standard Lisp, but now contains many more facilities. It is quite efficient in its use of both space and time, and has been optimized for algebraic computation. All PSL versions of REDUCE are distributed with sufficient PSL support to run on the given computing system. PSL is supported on many architectures and is an ideal system for those wanting to run REDUCE as a stand-alone system. The principal developer of PSL before it became Open Source was the Zuse Institute Berlin (ZIB). PSL REDUCE offers only a command-line interface.
Codemist Standard Lisp (CSL)
CSL is a newer Lisp system that continues to evolve and is now written completely in C++, which makes it very easy to port to a new machine. Like PSL, it is a faithful implementation of Standard Lisp and has been optimized for running REDUCE. It requires a very small memory partition for its Lisp support. Furthermore, most of the REDUCE facilities are supported as machine independent pseudocode, which is quite compact. In the worst case, the performance of this system is about a factor of two slower than PSL, though in many cases it matches PSL performance. However, the memory use is smaller. All CSL versions are distributed with sufficient CSL support to run on the given computing system. This is also an ideal system for those wishing to embed algebraic calculations in a C or C++ programming environment. The developer of CSL before it became Open Source was Codemist Ltd. CSL REDUCE offers both a graphical and a command-line interface.
Other Lisps
There is also experimental code in the SourceForge Subversion repository to build REDUCE on several other Lisps, including GNU Emacs Lisp, several versions of Common Lisp (SBCL, CLISP, CCL and ABCL), and a version of CSL compiled to Javascript and webassemply (to run using Node.js or in a web browser).

REDUCE version numbers and releases

The commercial releases of REDUCE had version numbers, the last of which was version 3.8 released in 2004. The Open Source releases of REDUCE available since 2008 do not have version numbers, but are now identified by their Subversion revision numbers. A REDUCE release includes all necessary binary files for a specific platform and releases are currently provided irregularly every few months for Microsoft Windows, Apple macOS and GNU/Linux (all at the same time). Every so often there may also be a release for a more esoteric platform, such as the Raspberry Pi!

A release is essentially a set of files built from a snapshot of the source code, which evolves on a daily (if not hourly) basis as the developers commit updates. The source code is managed using Subversion, which increments the revision number (of the whole code base) with each commit, and this now serves as a version number. Since the whole code base is now publicly available, formal releases are no longer very significant.