Phrase Meaning – ‘Pay Off’ vs. ‘Pay Up’: Understanding the Difference

There is an important difference not explicitly mentioned in those definitions: the grammatical subject of break off refers to a different agent than the grammatical subject of break up.

The subject of break off was previously participating in or causing the activity that ended. The activity ended because the subject stopped continuing it.

The subject of break up was outside the activity, not part of it.* The subject actively interfered with its continuation, causing it to stop.

For example:

The police broke up the fight.

means that some people, not the police, were fighting, and the police forcibly made them stop fighting. Most likely, the police physically grabbed the combatants, pulled them apart, and restrained them.

The police broke off the fight.

means that the police were themselves involved in the fight, and stopped fighting by their own choice. Perhaps the police were defending a building against a crowd during a public protest, and the police lost heart and decided to walk away and let the crowd do as it pleased. Or perhaps the "fight" was a negotiation to get a raise in pay. Then if the police "broke off" this fight, that would mean that they gave up trying to get the raise, agreeing to continue to work at their present salary.

When people "break off negotiations", this means that they refuse to continue negotiating. They have given up hope of making a deal, or they demand a concession from the other side before they will even continue talking. They have "walked away from the negotiation table."

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*Of course, there is also a different sense of break up, such as sense 2, the break-up of a romantic relationship, in which the participants do end it.

It depends on the context, if they can be used interchangeably.

A. In some cultures, it is rude to point at / point out a person.

If, by the above sentence, you are referring to the action of raising or directing the index finger at someone/something, then it should be

In some cultures, it is rude to point at a person.

Examples: She pointed [with her finger] at the map (one can also point with a stick, knife, or gun). He pointed in the direction of the town center. These examples are from Online OXFORD Collocation Dictionary, with some edits.

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B. She pointed at / pointed out an object in the sky.

This one depends on the context. If there is an object in the sky, then the following is valid:

She pointed at the object in the sky. OR She pointed at an object in the sky (if there are multiple objects).

These are both equally correct:

She pointed at her favorite star in the sky (with her finger). She pointed out her favorite star in the sky (by describing it - the brightest one).

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The phrasal verb "point out something" or "point something out" can be used in a number of ways.

Cambridge says to point something out is

• to tell someone about some information, often because you believe they do not know it or have forgotten it. Example: I pointed out that his visa would expire in 2 months and that he needed to apply for an extension asap.

• to direct attention toward something [or someone]. Example: Angela pointed out some spelling errors in my paper.

MW provides this example: He pointed his girlfriend out (to me) in the crowd.

C. She pointed at him to me / She pointed him out to me [may be by describing some characteristics].

We don't say "pointed at him to me". Just like the example from MW, it should be

She pointed him out to me (guy in a cafeteria - the one eating like a pig, guy in a group photo - the one with the silver smile, guy in the soccer field - the one who is always flopping). Example: John, eleven o' clock, the redhead, she is the one! Here, no finger is pointed, but characteristics are described to point out a person in a crowd.