Not really-really (JFYI).

Those are not properly "shutters", they are (as you say) "tapparelle" (which translates back to "rolling shutters" or "roller shutters"), they are relatively "modern" and they have been used for yers mainly as a low cost solution to the traditional windows "sets".

They were only widely adopted in Italy after WWII in new buildings.

They were actually available in Italy - and of course in wood only - since the '20's but not widely used, actually intially they were considered "trendy" and used by "name" architects/designers in luxury or public buildings (example):

https://en.wikipedia.org/wiki/Casa_del_Fascio_(Como)

, whilst later they became synonym with "poor/economic buildings".

They are not "typically italian", as they are common also in other EU countries and were most probably actually invented in France:

https://www.griesser.fr/en/products/rolling-shutters/

A famous example of their (early) use is Casa Milà in Barcelona (Spain) by Gaudì:

https://en.wikipedia.org/wiki/Casa_Mil%C3%A0

Interestingly our UK friends seemingly call them "continental" (another example):

https://www.ukrollershutters.com/product-category/continenta...

Traditionally in Italy (but it depends on the area/region) we have "persiane" (on the exterior), that can give some shade from the sun while allowing the air to pass, like these (example):

http://www.bglegno.it/linee-serramenti/persiane-legno/

Then the actual window (with glass panes) and finally the actual shutters, which are called "scuri" (or "scuretti"), like these (example):

http://www.bglegno.it/linee-serramenti/scuretti-in-legno/

They are internal and completely darken the room if closed.