In grammar, the 'al' of ta'reef is commonly described as being composed of ALIF and Laam. This can become hamzatul wasl in an Arabic sentence or Quranic ayah.

Question
In grammar, the 'al' of ta'reef is commonly described as being composed of ALIF and Laam.  This can become hamzatul wasl in an Arabic sentence or Quranic ayah.  If the alif of madd is the only true alif, should we really be calling the 'al' of ta'reef as Hamza and Laam then?

Otherwise, if we can interchange the description of a letter as hamza and alif, what are the real implications of the only true alif being one of madd.  Also, the Arabic alphabet taught does not include hamza.  It is assumed to be included with the alif.  Which is correct, and why does it matter?

Jazakamullahu khairan for this very hepful Q/A service.

Answer
The Arabs call it alif laam at-Ta'reef, but it is a hamzah wasl and a definite article lam.  This is what the Arabs have been calling it for a long time.
The hamzah here is a hamzah al-wasl and thus used only when starting the word, dropped when reading in continuum with what preceded it. 
There are many versions of the Arabic alphabet.  Some have the hamzah as a letter, others put in the lam-alif to show that the true alif is a medd letter, others put in an alif to cover both.
 It is better not to call a hamzah an alif, instead we should call an alif and alif and a hamzah a hamzah. 
Wa iyyaakum.
Wa assalaam