芦苇 is one of the oldest plant names in Chinese poetry - opening 《诗经·秦风·蒹葭》 (The Book of Songs, 'Reeds'): 蒹葭苍苍,白露为霜 ('The reeds are lush green, the white dew has turned to frost'). Both 苇 and 蒹 refer to reeds; 苇 specifies the mature plant.
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Both characters share the 艹 (grass) radical, marking them as plant names. 苇 alone also means 'reed' - 芦苇 is the standard two-character compound.