Correct

聊 vs 谈

/ liáo vs tán /
Strokes

Definition

聊 and 谈 are both Verbs, which mean “chat; talk”.

Example

谈 means "talk", it can be applied on occasion either formal or casual, whereas 聊 must be casual. The following examples concern serious matters, so 谈 is used.
Note: One can only say 谈话, not 聊话
1
Liǎng
guó
lǐngdǎorén
领导人
zài
tán
dào
duìfāng
对方
de
lǐng
领土
zhēngduān
争端
wèn
问题
shí
  
,
dōu
biǎoshì
表示
jiāng
píng
和平
de
fāngshì
方式
jiějué
解决
  

When it came to their territorial disputes,the leaders of two countries expressed that this should be solved peacefully.

2
Xiǎozhāng
小张
zài
gōngzuò
工作
zhōng
chū
le
wèn
问题
  
,
jīng
经理
yào
dào
bàngōngshì
办公室
tánhuà
谈话
  

There's something wrong with Xiao Zhang's work,so he was asked to have a talk with his manager.

3
yǒu
shénme
什么
wéinán
为难
de
shì
  
,
jiù
gēn
ge
哥哥
tán
  
!

If you have some difficulties, please tell me.

4
Shuāngfāng
双方
zài
yánjiū
研究
如何
zuò
合作
de
wèn
问题
shí
  
,
tán
de
hěn
kuài
愉快
  

The two parties had an unpleasant talk about their cooperation.

The following examples concern informal topics, so either words, 聊, and 谈 can be used.
5
jiǔ
喝酒
shí
  
,
liǎng
péngyou
朋友
tán
  
(
liáo
  
)
de
hěn
tóu
投合
  

The two friends talked very congenially over their drinking.

6
Xiǎozhāng
小张
  
,
zánmen
咱们
suíbiàn
随便
tán
tán
  
(
liáo
liáo
  
)
  
!

Xiao Zhang, let's have a chat.

谈 also means "discussion, talk", which can be used in set phrases.
Eg. 美谈 (story passed on with approval), 趣谈 (funny story), 奇谈 (strange tale).

It is also used in the title of a column of newspapers or magazines, eg.
《自由谈》(On Freedom)
《一夕谈》(A Day's Talk)
《一席谈》(On Conversation)
《古今谈》(On History)
7
xùn
鲁迅
zēng
xiě
guò
piān
tǎolùn
讨论
hàn
汉字
wèn
问题
de
wénzhāng
文章
  
ménwài
门外
wén
tán
  
  

Lu Xun once wrote an article discussing the issue of Chinese characters, "Menwai Wentan".

8
  
yǐnchá
饮茶
jīn
古今
tán
  
shì
běn
本期
zhège
这个
zhì
杂志
de
zhuānlán
专栏
  

"On Tea History" is a column in this issue of this magazine.

谈 can form some set phrases about activities concerning love and marriage.
9
men
他们
liǎ
zhèngzài
正在
tánliànài
谈恋爱
  

They are in love now.

10
duìxiàng
对象
tán
hǎo
le
méiyǒu
没有
  
?

Has she met her Mr. Right?

11
nián
tán
le
hǎo
好几
duìxiàng
对象
  

He changed several girlfriends a year.