One definition of public space or a public place is a place where anyone has a right to come without paying an entrance or other fee.
Typical examples are most roads, including the pavement, and public parks.
Typical differences between e.g. sitting on a public bench and sitting on a seat in a pavement café:
the first costs nothing
there is no time limitation
one can consume brought-along food and drinks (for alcoholic beverages the law prohibits this sometimes; this may even be the case if it is allowed in a pavement cafe)
a pavement cafe may have a dress code such as a prohibition of being shirtless, while in a public space only general law applies
The halls and streets (including skyways) in a shopping center may or may not be declared a public place and may or may not be open when the shops are closed. Similarly for halls, railway platforms and waiting rooms of public transport; sometimes a travelling ticket is required.
A public library is also more or less a public place, but some rules may apply which are absent outside.
In Sweden, all woods is considered to be public space, due to a law; allemansrätten; (everyones-right).
In general, there is no expectation of privacy in a public space.
Public spaces are attractive for budget tourists and homeless people, especially those that are relatively comfortable, e.g. a shopping center that provides shelter and, in a cold climate, is heated (or cooled in a hot climate). Sometimes the presence of homeless people is not appreciated and measures are taken to make the public space less attractive to them; the comfort of regular users may be affected by these people but also by the measures against them, e.g. no benches, a lower temperature, waiting rooms that are locked in the evening, etc.
A broader meaning of public space or place includes also places where everybody can come if they pay, like a cafe, train, movie theater, brothel, etc.
A shop is an example of what is intermediate between the two meanings: everybody can enter and look around without obligation to buy, but activities unrelated to the purpose of the shop are not unlimitedly permitted.
