Applying Style Overrides to a Jquery Plugin

Applying Style Overrides to a Jquery Plugin

My question directly is in concern to the following plugin, although the answer will help me deal with other plugins of the future:

http://plugins.learningjquery.com/cluetip/#options

Basically, I have 2 instances of this plugin used within my pages.  Physically, the 2 menu buttons are clsoe together.  So, with the default settings of the plugin, the cluetip that appears is not in the right place on one of the 2 instances.  So with the second instance needing some modification away from the default parameters of thhe plugin, where do I make that "override" for just that one instance out of the two -- the cluetip's CSS file or using the options/API that appears in the above link by citing the override by the corresponding div that the second cluetip is in?

Overall the concept of API within jquery specifically confuses me.  So when the above page is under a "API/Options" title for the page, it confuses me as to what is the API--the options detailed there, or what?  Im not visually editing these objects, (Im doing it by hand in code), so why do they call it API?