Meaning of “public affairs” and “public interest”

Question

The definition of political from OALD is:

connected with the state, government or public affairs

Is the definition of public of public affairs definition 1 or 2 or neither?

1. of, relating to, or affecting all or most of the people of a country, state, etc.
2. connected with the government and the services it provides

From dictionary.com, affairs is defined as:

matters of commercial or public interest or concern

Which of the following is the definition of interest of public interest?

1. the quality that something has when it attracts somebody's attention or makes them want to know more about it
2. a good result or an advantage for somebody/something

Answer 1

The use of both these terms can vary depending on context. Public affairs might relate to government policy, company policy, or simply function as a catch-all term for a relationship with the public (through, for example, the media). So, both of your listed definitions could be applicable.

Public interest, again, could cover matters which are of interest to the public or are considered to be beneficial to the public. IOW, both of your listed definitions could again be applicable.

Answer 2

"Public" in "public affairs" would be your definition # 1:

of, relating to, or affecting all or most of the people of a country, state, etc.

Here's an example: To be the director of public affairs means your work "involves events, activities, etc., that a company does for the public."

But if we take into account this other definition of "public affairs":

matters of general interest or concern, especially those dealing with current social or political issues

This definition will encompass/ include your definition #2:

connected with the government and the services it provides

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On the other hand, "interest" in "public interest" could be both your definitions.

As the Free Dictionary puts it more precisely:

public interest

n.

1. The well-being of the general public

2. The attention of the people with respect to events