Finish Up! Finish Off!

I have talked a lot about phrasals with up, lately. I do love them!! Don't you?!
Anyway, it means to finish a task completely.

Like: By the time you asked me out, I had finished up my job.

Another meaning is similar with end up, explained Here.

Like: I finished up in jail yesterday.

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It is also similar with finish off. It means to finish doing something completely.

Like: She finished off her job yesterday. After, she got in her home and finished off the cake.

The last illness finished him off. 

The verb on the last example means to kill. That's the difference between finish up and off meanings.

Got everything?!