Why does "public" refer to the government?

Question

I'm a non-English native and was quite surprised with the meaning of "public" refering to "belonging to government" or "provided by government", etc. In my past experience "public" was sort of an alias for "what you show to everyone / post on your SNS page" - or otherwise isn't kept in secret (which could be described as "private" things).
So previously I faced both "public" and "private" in a context related to one single person in question: to describe things they display to everyone (public appearance) or keep in secret (private life).

Most of all I was confused by using "public" term referring to governmental companies that do not provide any services to people and just produce some stuff, like smelting factories or other heavy industry - I mean, no way people from outside could use it in their daily life directly. Still, it belongs to the government and thus is being referred to as "public company". This blew my mind completely and that's why I'm here.

I tried to do some research to figure out the origins of this new meaning, but it seems like it is too basic and fundamental in English, so I managed to find only discussions of various "public affairs" or services and how they work.

So I would appreciate it if somebody could provide links or a detailed explanation of the origin of this meaning for the "public" adjective. Or maybe a historical background? Since I'm not sure which term comes first: 'government' or 'public'.

I would appreciate it as well if you provide additional explanation of possible differences between "belonging to the government" and "public", since I'm still not sure if they're 100% synonymous.

Answer 1

The Online Etymology Dictionary covers this fairly well [reformatted and comments added]. It is seen that the 'non-private' and the governmental senses were both present from very early in the life of the English word; 'transparent government' should perhaps be a tautology:

public (adj.)

late 14c.,

• "open to general observation," [contrast 'private'] from Old French public (c. 1300) and directly from Latin publicus
• "of the people; of the state; done for the state," [so related to government] also "common, general, public; ordinary, vulgar," and as a noun, "a commonwealth; public property," altered (probably by influence of Latin pubes "adult population, adult") from Old Latin poplicus "pertaining to the people," from populus "people" (see people (n.)).

Early 15c.

• as "pertaining to the people." [contrast 'relating to private concerns / enterprises'] From late 15c. as "pertaining to public affairs;" meaning "open to all in the community" is from 1540s in English. An Old English adjective in this sense was folclic.

Public relations first recorded 1913 (after an isolated use by Thomas Jefferson in 1807).

Public office "position held by a public official" is from 1821.

Public service is from 1570s.

Public interest from 1670s.

Public-spirited is from 1670s.

Public enemy is attested from 1756.

Public sector attested from 1949.

Public funds (1713) are the funded debts of a government.

Public school is from 1570s, originally, in Britain, a grammar school endowed for the benefit of the public, but most have evolved into boarding-schools for the well-to-do. The main modern meaning in U.S., "school (usually free) provided at public expense and run by local authorities," is attested from 1640s. For public house, see pub.

So there is a long-standing degree of overlap between the senses. Care has to be taken in using the word so as to avoid ambiguity where this would be serious. Context must be weighed carefully. One should be pragmatic.