domestic duck
Refers specifically to the domesticated duck, as opposed to wild ducks (鴨, かも).
公園の池にアヒルがたくさんいる。
There are many ducks in the park pond.
They keep ducks in the farmhouse yard.
アヒルの卵は鶏の卵より大きい。
Duck eggs are larger than chicken eggs.
池でアヒルが泳いでいる。
Ducks are swimming in the pond.
鴨 refers to wild ducks (and the duck family in general), while アヒル refers specifically to the domesticated duck raised for meat or eggs.
counter for birds; counter for rabbits
Katakana spelling is standard and most common; the word is usually written in kana.
Hiragana spelling, also common.
Rare kanji form; not commonly used.
Very rare kanji form; practically never used.
One common explanation derives あひる from 足広, “broad-footed,” through the intermediate form あひろ, referring to the duck’s broad webbed feet. Other origins have also been proposed.