Some say that the E-2 is an AEW (Airborne Early Warning) and cannot be called an AWACS (Airborne Warning And Control System) since the plane's ability to effectively perform a command/control role is very limited. Command and battle management is still being done from the carrier and the Hawkeye's role is primarily to provide radar system enhancement and augmentation.
The E-3 Sentry is a proper AWACS since it carries a more sophisticated and powerful suite of systems and have 13-19 specialists operating the mission control systems compared to the E-2 Hawkeye's 2-3. This allows it enough to effectively perform an autonomous command / control role.
Also, China is not the second country to indigenously complete development of a carrier borne AEW aircraft. US is first, I believe UK is the second, China will become third once KJ-600 finish development.
Here are some pictures of the earlier carrier borne AEW aircraft:
TBM-3W Avenger, the first carrier borne AEW plane.
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Fairey Gannet AEW.3, the first non-US developed carrier borne AEW plane.
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