what is difference between Internet Explorer (64-bit) and Internet Explorer on 64bit windows versions?
Basic 'Internet Explorer' will be the 32-bit application, which will run under a 64-bit environment through the standard 32-bit 'emulation' that is built into 64-bit versions of Windows (Without which no 32-bit program, such as almost all programs made in the last 20 years would run at all).
I don't know if there's any actual differences in the program interface itself, but running a 64-bit version means the program has access to more processing ability and can address more memory, although if IE needs more than 3.2 GB I'd be concerned.
In addition to @tjennings' answer, one major difference is that 32-bit native code doesn't run in a 64-bit instance of Internet Explorer, due to the lack of in-process thunking in Windows (see also thunk) and the fact that for example MSIE extensions execute within the MSIE process. Quoting Q&A: 64-Bit Internet Explorer on the (MSDN) IE Internals blog from back in mid-2009 (emphasis mine):
Q: Why? What does not work properly with 64bit IE?
A: Browser addons, including BHOs, Toolbars, and ActiveX controls, must generally be the same bitness as IE itself. So, if you are running a 64bit version of IE, any site that uses, say, Adobe Flash, isn't going to work until you install the 64bit version of the addon. Sadly, almost no browser addons are currently available in 64bit versions, although that's somewhat likely to change in the future as 64bit Windows becomes more prevalent.
The software availability situation has likely improved in the years since that blog post was written, but the technical reason why it is a problem in the first place remains.