noun
Refers to the part of a tool, utensil, or weapon that is held by hand.
包丁の柄が濡れていると滑りやすい。
If the handle of the kitchen knife is wet, it's slippery.
noun
Used for the stalk of a mushroom, leaf, or similar plant part.
しいたけの柄は固いので、料理によっては取り除く。
Shiitake mushroom stalks are tough, so they are removed depending on the dish.
取っ手 is a more general term for a handle or knob, often attached to doors, drawers, or lids, while 柄 specifically refers to a long grip held in the hand, like that of a tool or weapon.
The kanji 柄 is used for its meaning 'handle' or 'shaft'. The reading え is a native Japanese word (kun'yomi).