There is an EPSG code for a plain NAD83 -- EPSG:4269:
GEOGCS["NAD83",
DATUM["North_American_Datum_1983",
SPHEROID["GRS 1980",6378137,298.257222101,
AUTHORITY["EPSG","7019"]],
AUTHORITY["EPSG","6269"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.01745329251994328,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4269"]]
Per http://spatialreference.org/ref/epsg/4269/prettywkt/ and http://spatialreference.org/ref/epsg/4269/ and http://epsg.io/4269
EPSG:4326 differs per http://spatialreference.org/ref/epsg/4326/prettywkt/
GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.257223563,
AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.01745329251994328,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4326"]]
Drawing from http://www.uvm.edu/giv/resources/WGS84_NAD83.pdf -- The two datums use different spheroids, with the NAD83 tracking with the north american plate, while the WGS84 tracks with the center of mass of the earth. The centers of the two were coincident in the 1980s when they were originally defined, but have diverged 3-4 feet in since then.
There are also a number of other "NAD83" coordinate systems within EPSG. EPSG:4152 is NAD83(HARN), EPSG:4140 is NAD83(CSRS98), and a EPSG:4893 which is NAD83(NSRS2007)