Learn English – the difference in the meaning between “busy in studying” and “busy studying”

Here is an example I like to use with my students.

Sarah says, "I was doing my homework and my friend called."
Rachel says, "I did my homework and my friend called."

This means that Rachel finished her homework, but Sarah did not finish her homework. The "was doing" means that something was still going on, that it was interrupted or that it never finished.

For my info, you could see englishpage.com's article on this topic.

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.