A proxy is any server that makes a request on your behalf, so the destination sees the proxy rather than you. That definition covers several quite different things sold under the same word, and most confusion about proxies comes from two people using it to mean two of them. Sorting them out takes a paragraph each and settles almost every question that follows.
The three things the word usually means
A web proxy is a page you load another page inside; it covers that page only. A system or SOCKS proxy is configured in the operating system or one application, and routes that application's traffic through a server without necessarily encrypting it. A residential or datacentre proxy pool is infrastructure sold to businesses for automated collection at scale, priced per gigabyte, and has nothing to do with a person wanting privacy on a laptop.
The question that decides whether you want a VPN
Ask whether you need the traffic encrypted between your device and the server, and whether you need every application covered rather than one. If either answer is yes, you want a VPN: encryption of the whole device's traffic is precisely what it adds over a proxy. If both are no, and you simply want a different exit address for one application, a proxy is a smaller tool for a smaller job and there is nothing wrong with using it.
Why proxies are cheaper, and what you give up
A proxy does less work per byte than a VPN, so it costs less to run and is often free. What you give up is encryption, coverage and, on free services, any statement of what the operator keeps. The paid VPN market solves that by publishing a price and a logging policy on its own site, which is what this index reads and quotes, and the free proxy market largely does not.
Where the two overlap in practice
Several VPN providers include a proxy as part of the subscription: a browser extension, or a SOCKS5 endpoint for applications that want one specific route rather than the whole device. That is usually the sensible way to get both, since the proxy comes with the same published policy and the same company standing behind it as the VPN you are already paying for.
Questions people ask about proxy
Is a proxy the same as a VPN?
No. A VPN encrypts and covers the whole device; a proxy usually does neither, though it does change the address a destination sees.
Are proxies legal?
Yes, in every market this site covers. What you do through one is governed by ordinary law, exactly as it is on any other connection.
Do I need both?
Rarely. Several VPN subscriptions include a SOCKS5 proxy for the cases where you want one application routed separately.