The use of spider mite is just an abbriviation of Red SPider Mite, and as the above poster said, they are common on citrus and yes, they make webs; I've seen colonies make webs over several square yards. These mites are medium size, and there are others that you wont easily see even with a strong magnifying glass.
So the spider mites generally spoken of are herbivorous. There are many other kinds, and some are living on you right now on your eyelashes [img]http://www.**********.com/iB_html/non-cgi/emoticons/wow.gif[/img]
In greenhouses they use some kinds to eat other mites.