Both. A banana (the yellow thing you peel and eat) is undoubtedly a fruit (containing the seeds of the plant: see answer regarding tomatoes) though since commercially grown banana plants are sterile. The seeds are reduced to little specks. However, the banana plant, though it is called a banana-tree in popular usage is technically regarded as an herbaceous plant (or herb), not a tree, because the stem does not contain true woody tissue.
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