What is a "private proxy" vs a SOCKS, HTTP, HTTPS proxy?

I see the term "private" proxy used a lot. Just wondering what the difference between this, a "public" proxy and SOCKS, HTTP, HTTPS? Is the term "private" not dependent on whether it is a SOCKS, HTTP, or HTTPS?

public proxys can be farmed by anyone and require no password access
but there uses are limited and are usually abused.

private proxies are paid proxies usually req authentication login, have better
security than public proxies.

public proxies will likely leak data and there anonymity is poor
where as paid private proxies offer privacy

Public proxies have shared IPs, which means the proxy you're using can be used by 20 other users at the same time and therefore, these proxies get easily abused and blacklisted. Private proxies are dedicated to some extent but these proxies have a very limited IP pool. In some use cases (social media for example), static private IPs don't work too well.

SOCKS, HTTP, HTTPS proxy are protocols
HTTP can only use for browser-based protocol

Private is another things mean, Vs shared proxies Vs public proxies

The difference, as far as I know, is about the limit of people with whom they share proxy addresses. If the total ip pool of the site is 10k, under normal conditions, if they sell these 10k proxies to 1 person, they must demand very high money, but they sell the same ip pool "shared" proxies to more than one person. Some sites state that it can be shared with up to 3 people and up to 20 people. Private are just the proxy addresses they assign to you.