FTP is "file transfer protocol".
It's a old fasion way to transfer files between computers. It has security issues because it transmits plain-text passwords, so it's not that usefull for Internet stuff anymore, except for anonymous downloads. For LANS and such it's acceptable. It allows you to not only download files, but to upload and modify files and directories on a server.
A Proxy is a program (or computer) that acts like a "proxy" (or a go-between/middleman) between one network and another. Commonly used for HTTP (world wide web traffic) in businesses to filter out bad content such as porn and viruses. also used as a performance enhancer/bandwidth saver thru cache'ing webpages for local network copies. Also used online to try to preserve anonymous surfing and for connection sharing. (although most home routers and networks now use NAT or NAT-like technology to allow computers on private networks to access the internet.)
a example proxy program
To transfer files in between Windows computers you generally use "Windows File and Printer sharing" stuff based on a SMB protocol. This is fairly normal, look on the internet for "file and print sharing".
This is for LAN use only and needs to be protected from the internet by a firewall or a poses a significant security risk.
You can use other methods like installing a FTP server on one of the Windows machines, but it's easier to File and Print Sharing.
Webopedia is a good place to find definitions for technical terms and links to more information.
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www.webopedia.com