Learn English – Meaning difference between Wandering and Roaming

The two terms are closely related, and even interchangeable in many cases. However, the two words focus on different things. Alliance is more about mutual interests or benefit, while coalition is more about doing some action.

The use of both terms is not limited to the political context. They can be used in other contexts: military, financial, commercial, technological, and so on. Having said that, I agree that coalition is used most often in the political context for "a temporary alliance of political parties forming a government or of states" (see below).

Here are their definitions, according to Oxford dictionary:

alliance (noun)
1. A union or association formed for mutual benefit, especially between countries or organizations.
1.1 A relationship based on similarity of interests, nature, or qualities.
1.2 A state of being joined or associated.

coalition (noun) A temporary alliance for combined action, especially of political parties forming a government.

Here is a quote from Get Them On Your Side by Samuel B. Bacharach (chapter 5):

Formally defined, a coalition is a politically mobilized collection of interest groups or individuals committed to achieving a common outcome (i.e., resistance or change). Through political mobilization you create a group that has some sense of shared goals and/or a sense of connected interests. A coalition is an alliance for joint action.

In short, a coalition is an alliance for joint action.

In many contexts, the meanings are pretty much the same, but you might hear finished more often than completed in casual conversation. For example:

I've finished my shopping.
She finished the song.
He finished the race.

I could use completed in those sentences – the meaning wouldn't change, but the register might sound off.

The word completed can convey some sense of accomplishment. In the context of a race, it might work when the race is a major achievement:

He completed his first marathon last year.

Homework, though, is not really a major achievement, so I think you'd hear finished more often in casual conversation:

“Joey, where are you going? Did you finish your homework?”

That said, you might see completed in more formal contexts, such as a paper on education, or a course syllabus:

Students must complete six homework assignments during the semester.