My textbook says that alligator is わに. I checked the kanji and it turns out to be 鰐.
When I checked the Japanese for crocodile and alligator they seem to be the same, either 鰐/わに or 鰐魚/がくぎょ.
Is there a distinction between alligator and crocodile in Japanese ?
What is the difference between わに and がくぎょ ?
You can safely forget the word 鰐魚【がくぎょ】, which is basically not used in Japanese, unless you read Classical Chinese literature.
Just as you noted, 鰐【わに】 is the only native word that covers all crocodilians, and is preferred in Japanese over any subdivision such as alligator, caiman, crocodile, gharial etc.
