Both models minimize total inventory cost — but one assumes your stock shows up all at once, and the other assumes it trickles in while you're still using it.
Economic Order Quantity (EOQ) and Economic Production Quantity (EPQ) are the two classic lot-sizing models every industrial engineer learns, and they get confused constantly because the formulas look almost identical and both answer the same question: "how much should I order or produce at a time to minimize total annual inventory cost?" The difference that actually matters is a single assumption about how replenishment arrives— instantaneously, or gradually while demand keeps eating into it. Get that assumption wrong and you'll size a production run using a formula built for a supplier delivery, and understate your required batch size.