One way to hold cornet: a little horn. Narrow and closed at one end, wide and open at the other, opening out smoothly in between. Put your lips to the small end and blow, and it is a musical instrument. Turn it up the other way and drop ice cream in the wide end, and it is the wafer cone in a child's fist on a hot afternoon. Both are the same shape, named the same way.
From the word’s history
Wiktionary gives cornet from Middle English and Old French cornet, a diminutive of a reflex of Latin cornū 'horn'. The diminutive is the whole story: a little horn.
字源資料記錄 cornet 來自中古英文與古法文的 cornet，是拉丁文 cornū（角）小稱形式的後代。關鍵就在那個「小稱」：小小的角。這條線索直接解釋了樂器和冰淇淋筒為什麼共用一個字。
Wiktionary/kaikki extract supplied in this evidence packet (source_ref kaikki:3f6f69a190036ae4:281950200): 'From Middle English cornet, from Old French cornet, a diminutive of a popular reflex of Latin cornū (horn).'
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