Loanwords can change meanings after borrowing. “Pasta” in German and English refers the Italian specialties, while pasta in Italian means any kind of noodle and even some dumplings. “Noodle” kept its meaning in English from German nudel / Dutch noedel.
It is the other way around, a noodle is a type of pasta.
Pasta literally means paste, it refers to the dough pasta is made from. Is fact, it also means dough and pastry.
Loanwords can change meanings after borrowing. “Pasta” in German and English refers the Italian specialties, while pasta in Italian means any kind of noodle and even some dumplings. “Noodle” kept its meaning in English from German nudel / Dutch noedel.
If you want to properly classify things it is good to know where words come from.