They're actually very different.

The 'a' sound in 'as' is the same sound from 'cat', 'mad' or 'sad'.

The 'u' in 'us' is pronounced like you'd expect ie. it's the same as the 'u' in 'up', 'under' and 'run'.

The 's' sound from 'as' is a 'z' sound, as in 'zoo',

The 's' in 'us' is a normal 's' sound. It's just like the 's' in 'say', 'so' and 'six'.

They don't have the same sound, Federico. To the native speaker they are completely different sounds. They only seem different because you are 'filtering' the sounds through an 'Italian ear'.  Listen to more English - try to forget the phonology of Italian - and you will soon hear the difference.

First of all, no, these two words don't sound alike. Even to my Indonesian ears.

Second, don't bother too much. When we listen to someone speaking, we don't hear it word per word. We understand it as a context. Most of time, in a conversation, we even understand the context first <em>and then</em> realize what the words are. Us and as are used differently and have completely different meanings, they are impossible to misinterpret. 

Lastly, if you want to learn a language, stop telling yourself that this language is crazy difficult because bla bla bla. The rules aren't gonna change. It is what it is. So, instead, try to find a way to comprehend it. 

Buona fortuna!

Federico:

 You are much mistaken.   AS  and US  do not have the same sound.

 I do not know where you came by this information, but it is errant.

   In AS   the S is pronounced as a Z.    

   In US,   the S is not pronounced as a Z.

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    In  AS,  the A is pronounced the same as it would be in the following words:

  AT,  CAT,  FAT,  BAT,   SLAT,  FLAT,  

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   In US,  the U is pronounced  as it is in  But,    Cluck, Much,  Suck,  and Duck

.

  Where are you getting your information?

.

They should not sound exactly the same. :-)

If you listen to how "has" is pronounced compared to "bus" the different tones are easier to hear.-----chartill

    Those are particularly good examples.   They are much better than mine. Very good indeed!