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I've read that both the ～てしまう and ～きる (18th meaning of 切る at
<http://www.csse.monash.edu.au/~jwb/cgi-
bin/wwwjdic.cgi?1MUE%E5%88%87%E3%82%8B>) forms are used to signify something
has been finished/done/completed.

If so, what exactly is the difference between the two conjugations (how do we
decide when to use which)?

example:

1) もう荷造りしてしまった。

2) もう荷造りしきった。
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grammar usage nuances conjugations て-form
What exactly is the difference between <verb>-てしまう and <verb>- [切]{き}る?
_Added: This answer was written in response to the revision 1 of the question.
It turned out that the answer was not very relevant to the question which
Pacerier wanted to ask._

-てしまった is the past form of -てしまう, and it means completion. It often implies that the action is undesirable.

> 皿を割ってしまった。 (さらをわってしまった。) I broke a plate.

-てきた is the past form of -てくる (not -てきる). The original meaning of くる (来る) is to come, and the form -てくる means that some action is done in a place other than here, with an implication that the actor will come back here after the action is completed (see the sense [17]-(イ) in [Daijirin](http://dic.yahoo.co.jp/dsearch?enc=UTF-8&p=%E3%81%8F%E3%82%8B&dtype=0&dname=0ss&stype=1&pagenum=1&index=105627000000) and the sense 9-(3) in [Daijisen](http://dic.yahoo.co.jp/dsearch?enc=UTF-8&p=%E3%81%8F%E3%82%8B&dtype=0&dname=0na&stype=1&index=06504705274200&pagenum=1)). -てきた means that the action was done in somewhere else and the actor came back.

> コーヒーを飲んでくる。 (コーヒーをのんでくる。) I will drink coffee and come back. (=I will take a
> coffee break.)

In your examples, 荷物をもう荷造りしてしまった implies that it is a bad thing. Probably the
speaker packed the baggage, thought that he/she was ready for a trip, and
realized that he/she had forgotten to put something in it (therefore he/she
has to redo the packing). 荷物をもう荷造りしてきた means the packing was done in somewhere
other than here.

(By the way, in these examples, 荷物を sounds redundant to me, because if you say
荷造りする, it is obvious that the object is 荷物. I do not think that it is
incorrect, but it may be better to omit 荷物を.)
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Not a true answer, but {verb}てしまう has the nuance of the action has complete
coverage on the object/subject.

> 勇者たちが滅んでしまった。  
>  The hero party is annihilated.

In the example above, it implies that not a single one member of the hero
party is left. It has the extra feeling of "sadness, regret" that such thing
happens.

Meanwhile, {verb}きる is for notifying a course of action has completed all the
way to its final stage.

> 義理でもらった零ちゃんのチョコレートはまずかったけど、ちゃんと最後まで食べきった。  
>  The chocolate I got from Rei-chan out of courtesy was not tasty, but I ate
> it to the end.

Here is another idiomatic usage.

> あなたの恩は感謝してもしきれないぐらい。  
>  Your deed, even if I thank it, I can never thank enough.

(edited: previously, it was 感謝したくても, but as Tsuyoshi Ito pointed out, it would
mean that the speaker didn't manage to thank. But not only that, it may imply
the following:

> 感謝したくてもしきれない。だからあえて感謝しない。  
>  I can't thank enough even if I want to thank. Therefore I choose not to
> thank instead.

oh, what arrogance!)
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First, the ～てしまう construction can convey a sense of regret, which the 切る verb
suffix cannot:

> 花瓶を落として割ってしまった。 I dropped the vase and [regrettably] broke it.
>
> 花瓶を落として割り切った。 (unnatural)

When used in constructions expressing the completion or finishing of an
action, 切る tends to sound best with actions that can be measured on a scale,
but there's a lot of overlap:

> 使い切る use up (使ってしまう could work)
>
> 乗り切る completely overcome (乗ってしまう sounds unnatural)
>
> 冷え切る cool off entirely (冷えてしまう could work)
>
> 疲れ切る become exhausted (疲れてしまう could work)
>
> 出し切る put forth everything (出してしまう might work in some cases)

All of the verbs above imply the exhaustion of a finite quantity (使う, 疲れる, 出す)
or a change that could stop at any point on an invisible scale (乗る, 冷える). This
aspect is reflected in the fact that the generic verb for "run out" is 切れる:

> ノートパソコンの電池が切れた。 My laptop's battery died.
>
> おい、この納豆の賞味期限が切れているよ。 Hey, this nattō's past its expiration date, you know.

On the other hand, for actions that don't fit into a nice scale (i.e. they
either happen or they don't), the ～てしまう form is usually better:

> 泣き出してしまう burst into tears (泣き出し切る sounds unnatural)
>
> 変わってしまう change completely (変わり切る might work in rare cases)
>
> ほれてしまう fall head-over-heels in love (ほれ切る sounds unnatural)
>
> 消えてしまう disappear entirely (消え切る might work in rare cases)
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