"Independent" means the battery didn't report to a higher organization such as an artillery battalion or regiment. For instance, the 13th New York Light Artillery was labeled independent, whereas Battery "H", 1st Rhodes Island Artillery Regiment was not.

Field artillery was distinguished by its equipment. For particulars, here's a website on that subject:

http://xroads.virginia.edu/~UG97/flags/artillery.html

Some of the United States units were pre-war regular army. However, many more units were raised by the regular army during the war.
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