There is a website that tells you literally everything about your Mac model as long as you have the model or serial. I searched yours and have pasted the link below for you to check out. It looks like you do have a unibody model. The difference was just how the MacBook was built (using a single hollowed block of aluminum or piece by piece).
https://everymac.com/systems/apple/macbook_pro/specs/macbook-pro-core-2-duo-2.93-aluminum-17-early-2009-unibody-specs.html