Proxy x NAT

[Muhamad Salem Sugui]

    Hello.
    Recently I send a question asking how NAT works. But now, I'm
confused.
    What is the difference between NAT and Proxy?
    If I set a Internet Connection Sharing in my LAN, this machine
sharing connection (gateway) is performing NAT or being a proxy?
    In time, thanks to everyone that send me suggestions.
    Thanks in advance.

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  Muhamad Salem Sugui