Simple English question

I am going out..............................我正在去外邊
___to buy___some cigarettes........[ to buy ]infinitive phrase不定詞短語 ] 修飾說明正在去緊外面買一些香煙. to buy 最适當,因為[ infinitive 不定詞 ]的動態特性是遲過原動詞going.


buying [ gerund 動名詞 ] 不适用,因其動態特性是先過原動詞going.就有矛盾.

如果用for就唔需要+to buy. 因為for已有去買 的含意.
I am going out ( for some cigarettes.)...... prepositional phrase介詞短語
修飾句前.爲咗一些香煙而外出.

I guesss you mean:

1. I'm going out to have(smoke) a cigarette.

or

2. I'm going out for a cigarette.

or

3. I'm going out for having(smoking) a cigarette.

First of all, usually use singular to indicate you take a break, using plural (s) sounds like you're going to continue smoking on and on...

1 and 2 are almost identical in meaning.
3 may not have grammar error, but nobody say like this.

for + verb + ing
applies to a reason rather than an action.

1. He was released from prison for having good behaviour.

2. I become ill for eating too much.

[For these sentence, no such writing with "to + the same verb"]

This may be just one difference I can think of to answer your question. So they are not interchangable and you cannot write the same sentence by filling in the two and ask about the difference. One of them must be wrong.