Phrasal verbs are not only for spoken English. They are used for emphasis, But their uses are based more on the type of speech and/or writing. "look up to" would be used in a more informal situation, where as "continue" might be used more academically or technically. This is the same for most phrasal verbs. Which might be used, depends on the situation the language finds itself in. Using the phrase "get through with" would be a good way to draw attention to asking someone to finish. But it sounds a little more abrupt than "finish" which would be more polite. ie... "Get through with it already!" verse "Can you finish up quickly." The second sentence is more polite and would be used in more formal situations. I hope this helps. ~Samantha :)

yes, they mean the same