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These are the sentences:

> ユニオンへサンドイッチを買いに行きました。
>
> ユニオンへサンドイッチを買って行った。

Are they both grammatically correct? Also do they both mean the same thing,
which by my translation is "I went to the union and bought a sandwich."

Do they only differ in their formality with the second sentence being more
casual?
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2014-01-18T14:58:48.000
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2014-01-18T19:27:12.783
2020-06-17T08:18:27.500
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question
grammar translation formality
Are both of these sentences grammatically correct? (stem+に+行く vs て+行く)
You are comparing apples with oranges. Let me compare

> サンドイッチを買ってきた。  
>  サンドイッチを買いにきた。

instead and hopefully this answers your question.

The first construction means that one action happens after the other. You
bought a sandwich and came (home).

The second construction means that you performed the second action to achieve
the first. You came to buy a sandwich.

Both sentences can be stated in the polite form, without any change in
content:

> サンドイッチを買ってきました。  
>  サンドイッチを買いにきました。
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2014-01-18T15:55:01.553
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2014-01-18T15:55:01.553
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answer
> ユニオン(or [生協]{せいきょう}?/大学生協?)へサンドイッチを買いに行きました。

sounds fine to me. It literally translates to "I went to the union to buy a
sandwich." Its casual version would be:

> ユニオンへサンドイッチを買いに行った。

* * *

Your second sentence;

> ユニオンへサンドイッチを買って行った。

sounds a bit awkward to me. It sounds to me like "I bought a sandwich and went
to the union." (parsed as ユニオンへ（サンドイッチを買って）行った。>> サンドイッチを買って、ユニオンへ行った might
sound more natural but it also means "I bought a sandwich, and went to the
union".)

買いに行った is like "went to buy" whereas 買って行った is like "bought and went".

As a side note,

> ユニオン **で** サンドイッチを買って行った。(へ-->で)

would be "I bought a sandwich at the union and went (somewhere)"; "I bought a
sandwich at the union on the way (to somewhere)"
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2014-01-18T17:00:17.987
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2014-01-18T17:00:17.987
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answer