TexEdit and Text Edit are two different programs, of course. The OS comes with TextEdit included. Tex-Edit is a rather old but still supported plain text editor, haven't used it in many years, however. Text Wrangler is a much better tool, IMHO.
However, your question contains multiple references to html and XML which are completely separate from the problem of displaying Word created RTF files in different apps/OSs. "html" as well as XML (and actually every other interpreted language) are simply plain text files. Some plain text editors may be able to also import/read/display and even write RTF. But that's a non plain-text function and not what
text editors are normally used for. Likewise, RTF has no use as html,XML, PHP, etc. Thus, I am totally confused about what html, XML, etc. has to do with your original question.
No app, on any OS, will be able to display 'foreign' 'characters' unless that language (and its numerous scripts) are installed on that computer. And, since it can't
display them, you cannot be sure that they will be written to the file correctly. You'll need to open the file in an OS that can recognize the 'character' codes for the 'characters' you first intended to be sure.
'Characters' are simply a number (usually hexedecimal) that are arranged in a specific order/format determined by the apps developer(s). If that format is 'open-source' or commonly used, any other developer can write a program to use that format for whatever purpose she might choose, maybe even for editing said files!
Of course, when one developer chooses to keep the format/order/modifiers/etc. secret, other developers have to 'reverse-engineer' the file to figure out what was originally intended. While MS does publish the format of RTF, it is not too speedy about it and may not actually publish absolutely all the details. That's their choice, of course...they invented it. But it does make it difficult for others to re-create the original 100% accurately. Thus, part of your seeing different things in different OSs and apps.
Of course, the language support issue seems to also be present. So, even if all your apps could work 100% accurately with any MS RTF output, you'd still not see the same things as the computer simply doesn't have the files that relate a 'character code' to any specific graphic that it uses to display that 'code.'
So, even if you have installed the latest Windows OS on your Mac, it still may have different language support files than the Mac OS. You cannot, therefore, expect to see the same display when using the same RTF on both OSs. No matter what app you use on each side. Period.
As I understand it, "RTF" is not magic. It can only create a file with characters that you can type from the keyboard. If you do not have language support for a particular 'character', you cannot type it into the file. Period. "RTF" is not simply another plain text file, it has special, non-printing codes that replicate certain styling functions such as
bold,
italic,
underline, etc. and
combinations of those. Nor does it have any concern for the language you might be using, it just takes the codes generated by the keyboard via the OS.
In my opinion, your choices, in order of simplicity, are:
1. Use plain-text, onlyHowever, this does not address the differences in languages on each OS
2. Use a word processor that has versions on each OS you might useHowever, this does not address the differences in languages on each OS
3. Make sure all OSs and apps used have exactly the same language support and can all read and write each others output
Finally, html, XML, etc. are completely separate and independent of the above issue and, IMHO, should be discussed in a different thread.
