Correct

姑娘 vs 女孩子

/ gūniang vs nǚháizi /
Strokes

Formula

1
大姑娘
2
老姑娘

Definition

姑娘 is a Noun and 女孩子 is the Endocentric Phrase (偏正短语), which both means [girl].
 

Example

姑娘 and 女孩子 both mean "girl"; 姑娘 can be used as an address, but 女孩子 cannot.
1) In examples ① and ②, the two words are interchangeable.

2) In example ③, it is an address, so only 姑娘 can be used.
1
ge
那个
niang
姑娘
  
(
háizi
女孩子
  
)
chuānzhāo
穿着
hěn
shímáo
时髦
  

The girl is in fashion.

2
niang
姑娘
  
(
háizi
女孩子
  
)
cháng
长大
le
  
,
zǒng
yào
jiàrén
嫁人
de
  

A girl is likely to get married when she is grown up.

3
niang
姑娘
  
,
yào
mǎi
zhǒng
miànliào
面料
  
?

What kind of cloth would you like,Madam?

姑娘 can mean "daughter"; 女孩子 occasionally means "daughter".
姑娘 is often used juxtaposed with 儿子 or 小子, while 女孩子 with 男孩子, or by itself.
4
jiā
他家
gèr
一个
  
儿子
  
,
niang
姑娘
  

He has a son and a daughter.

5
shēng
le
nánháizi
男孩子
  
,
háizi
女孩子
  

She has a boy and a girl.

6
jiā
他家
zhī
shēng
le
niang
姑娘
  

He has a daughter only.

姑娘 sometimes means "a woman who is never married", usually preceded by 大 or 老.
大姑娘 老姑娘
7
shí
四十
duō
le
  
,
háishi
还是
  
(
lǎo
  
)
niang
姑娘
  

She is single though she is forty years old.