In the case of using Word the formatting instructions are understood by Word and stripped off when Word takes that data and presents it on your screen. When you do a cut and paste all you get is the text from the screen. Pasting it to Mudcat is no different than typing it in by hand.
The basic difference is that word processors use a different methodology for formatting than browsers do. Browsers use tagging to tell the browser when to bold, italisize, center,etc. (Different browsers are free to present tagged info any way they want.) The benefit of the tagged method is that there is a standard and therefore any browser can be coded to present the text in the format prescribed by the tags.
Each word processor has it's own standard. That's why it is difficult (impossible) for one word processor to display a document created in another word processor. Heck, sometimes different versions of the same word processor have the same problem.