redhat cygwin vs cygwin? any difference?

From the Wikipedia page _{I've changed the links for this context,}

Cygwin was originally developed by Cygnus Solutions, which was later acquired by Red Hat. It is free and open source software, released under the GNU General Public License version 2. Today it is maintained by employees of Red Hat, NetApp and many other volunteers.

Red Hat Cygwin is at release 1.8 at the moment (cygwin.dll),
This is when the regular Cygwin is at release 1.7.7 (cygwin1.dll).

The Cygwin library, utilities, and numerous applications are available for free download under the terms of the GPL. Red Hat offers developer and user support for this software, as well as license contracts for the Cygwin library and its utilities. The Red Hat Cygwin official installation utility can be used for both initial installation and automated updating.

From the Cygwin FAQ,
Can I bundle Cygwin with my product for free?

Only if you comply with Cygwin's license very carefully. If you choose to distribute cygwin1.dll, you must be willing to distribute the exact source code used to build that copy of cygwin1.dll as per the terms of the GPL. If you ship applications that link with cygwin1.dll, you must either provide those applications' source code under a GPL-compatible license, or purchase a cygwin license from Red Hat.

Can I build a Cygwin program that does not require cygwin1.dll at runtime?

No. If your program uses the Cygwin API, then your executable cannot run without cygwin1.dll. In particular, it is not possible to statically link with a Cygwin library to obtain an independent, self-contained executable.

If this is an issue because you intend to distribute your Cygwin application, then you had better read and understand http://cygwin.com/licensing.html, which explains the licensing options. Unless you purchase a special commercial license from Red Hat, then your Cygwin application must be Open Source.