I have heard several different ways to say 'but' in Chinese and asked my teacher to explain the different ways that they are used.  

The easiest way to represent the difference is like this: (or remember based on photo)

不过 bù guò = ~~

可是 kě shì = :(

但是 dàn shì = -><-

Here are the differences in how they are used with example sentences.

不过 bù guò is generally a 'softer but', hence the wishy-washy ~~.  Basically you want to use this when you aren't sure or it's not that strong of a conflict. (~only, ~merely, ~anyway)

我很想去北京...  不过  ... 我还有学习.

wǒ hěn xiǎng qù Běijing búguò wǒ háiyǒu xuéxí.

I want to go to Beijing but I still have to study.

可是 kě shì is used frequently in spoken Chinese and is usually associated with something unfortunate, hence the unhappy face :( - I want something but unfortunately...

我很想去北京...  可是  ... 我没有钱  

wǒ hěn xiǎng qù Běijing kě shì wǒ méiyǒu qián.

I want to go to Beijing but I don't have any money.

但是 dàn shì is more formal, you'll hear it on the news and is usually used when the 'but' is very strong or the two are incompatible = -><-.

我很想去北京...  但是  ... 我的妈妈不让我去  

wǒ hěn xiǎng qù Běijing dàn shì wǒde māma bù ràng wǒ qù.

I want to go to Beijing but my mother won't let me go.

And just in case this post gets traffic from the photo or a misspelled word, here is how to say 'butt' in Chinese:

屁股 pì gu - butt / ass / bottom

And pì gu sounds a little like Pikachu.

Perhaps someone can explain the different uses of these butts in the comments - 

腚 dìng - butt

臀部 tún bù - butt / buttocks

Related post: How to say 'Either' 'Or' in Mandarin - difference 或者 and 还是

Image credits:

Attack of Titanic Asses Color by Omeganaruto34

Pikachu likes big butts by ryuskrew

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