What are the differences between [ fact ] and [ really ] ?

首先從詞的類形看fact和really已經是不同的，因為fact是名詞，而really是副詞，就算real也只不過是形容詞

除了詞性不同外，它們的意思是相近的
fact的意思是：事實、真相、實情和論句
它的英文解釋是：1)something that has happened or been done
　　　　　　　　2)sth. known to be true or accepted as true
　　　　　　　　3)(單數，無不定冠詞）reality；what is true；what exists：現實；真實的事物；存在的事物

第３種的意思，就與real的名詞reality相同

而really的意思是：真的，真地，實際上
它的英文解釋是：in fact; without doubt; truly

在這裏順便贈你一句片語，非常好用，就是：as a matter of fact（事實上）

As a matter of fact, I have never been there before.（事實上我從未到過那兒。）
Really, I have never been there before.

fact is a noun, states that something is true and real, and can be backed.
the sun is very hot. this is a true statement. there are information that supports the idea.
the sun is very cold. this is not a true statement. it cannot be backed. therefore, it's not a fact.
in fact, i went to the beach this morning.
the diamond, in fact, is real. somebody has inspected it.

really is a word that describes.
the diamond is really expensive. it is very expensive.
they are really going to fight. for reals they will fight.

real is not a noun. it is also an adjective, stating that something is exist, not imaginary or fake.
santa claus is real.
my dreams seem so real.

Actually they have different usage.......

[ FACT ] is a noun, whilst [ REALLY ] is an adverb.

To make it simple..... here`s an example that can tell the difference :

eg : Is it REALLY a FACT ?


hope it might help.