They look very different from one another. astice as having a .. blue colour ...aragosta .. reddish body, five pairs of legs, ...
To me it looks like a giant insect.
In English, however, they are both called lobster....
I were to invite an Italian friend to a Boston restaurant and order lobster for both of us, she might be dismayed at seeing an astice on her plate.
Hi, Mary-Lou, in your question you have all the elements you need to explain the mystery: let's start with your correct impression of a giant insect you inherited from your Latin ancestors:
The English common name 'lobster' is, as you quote,
a corruption of Latin locusta f (genitive locustae); first declension:
- locust, grasshopper
- crustacean, marine shellfish, lobster
So, the Latins thought that crustacean shellfish looked like giant insect , crickes, grasshopper,locust etc..., and, though the English words appear different now, they are both an adaptation of the same word ' locusta' => OE lopustre => lop[y]ster , and with the voicing of /p/, eventually = lobster . (Source: Shorter Oxford Dictionary )
The Italian word 'aragosta' derives from the same Latin word through the agglutination of the article [l]a-locusta] => l' alogosta (an inverse phenomenon occurs in "all' amatriciana => alla matriciana")
The second element you need is taxonomy: the Italian language is rich in common names because it's so easy to italianize Linneus' Latin terms of scientific classification: therefore you have : aragosta, astice, omaro, palinuro, gambero di mare etc, and can distinguish families and species., the English language overcomes this handicap using qualifiers. That's almost all, but let's examine the problem in detail:
#order# (...five pairs of legs...) ,The order in question is
Decapoda, and an infraorder is
Astacidea (from which you derive 'astice') which includes five superfamilies, one of these is:
Nephropoidea, which contains the families
Nephropidae, or Homaridae, and
Palinuridae, or 'spiny/ rock lobsters'
#genera#
the genus Homarus (from which you derive 'omaro') includes two species: " the American lobster (H. americanus) and the European lobster (H. gammarus), they are very similar and may have speciated as recently as the Pleistocene, during climatic fluctuations.The best characters for distinguishing them are the geographic distribution, with the American lobster in the western Atlantic and the European lobster in the eastern Atlantic, and by the presence of one or more teeth on the underside of the rostrum in the American species"
the 'American lobster' is also known as true lobster, Northern lobster, or Maine lobster and it is not true that it is only red in colour, in Italian: 'astice americano'
the 'European lobster' , or 'common lobster' is called in Italian : 'astice' or 'astice europeo'
Palinurus is a genus in the family of Palinuridae, and
Palinurus elephas/ vulgaris is "commonly caught in the Mediterranean Sea. Its common names include European spiny lobster, crayfish or cray (in Ireland), common spiny lobster, Mediterranean lobster and red lobster..
This species is called in Italian: 'aragosta [mediterranea]'
#ordering# In conclusion, as I said, Italian has different words whereas English has different qualifier: astice, omaro = true lobster, claw lobster, aragosta, palinuro = spiny lobster, rock lobster. "aragosta" has no claws, the English term is more descriptive
no claws : 
If you are treating a friend in Boston you probably have no chance of getting your aragosta, but you can order something quite similar, a Palinurus interruptus, that is a: California spiny lobster.
buonappetito!