The Legend of Zelda comic actually follows the story and events of The Adventure of Link, and uses characters from the Zelda cartoon series.
Nintendo of America’s official ALttP comic ran in Nintendo Power, and was created by Shotaro Ishinomori. It stayed true to the original story, yet created many new sub-plots and characters. You can read the full comic here.
The Japan-only manga series is published in black and white, and expands on the storylines offered by the Oracle games, Ocarina of Time, and Majora’s Mask.