Textarea is a standard HTML element and so was invented just after the dawn of time. Unfortunately this means it is limited in it's appearance and functionality.
Changing the colours of specific words is not possible as far as I know. However a way to get around this would be to have an iFrame embedded in the page. That way, you can treat the iFrame content as another web page and style it using CSS.
The Yahoo RTE, the FCKEditor and the Lightweight RTE works in this way.
Another option, which does not use an iFrame is the editor used here on Stack Overflow, known as the WMD. The files are here.