A pre-fetched open is a NHI open where the image is retrieved by some sort of automation prior to the user seeing the email. Describing it as prefetched implies that the users mail client won't fetch the image again when the mail is read by a human, rather it'll use that copy of the image it's already got.
A proxied open is where the entity that wants an image doesn't fetch it directly, rather it asks another system - the proxy - to fetch the image on its behalf. That means that the IP address fetching the image will be that of the proxy, and the browser metadata such as user-agent will be that of the proxy.
Proxies provide uncertainty about what IP address a human was using when they saw the email, and what browser or mail client they use, eliminating some tracking techniques.
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