I have no direct experience, but if the thing was built for a particular vendor, and isn't a 'generic' version sold to everyone, it will have a different number...may be an extra digit or letter or some other change. The stores do this partly for price matching, even though it may be identical (or not), to them, it's not identical unless the entire part numbers are identical. It depends, sometimes, it's just which label the put on it, but sometimes it's actually different. For example, Home Depot sells GE WH (at least where I live), but if you happen to call the 800 number listed in the manual, they answer the phone Rheem. One difference is the ones labeled Rheem tend to have a brass drain valve, those at HD labeled GE, tend to have a plastic one, or at least a plastic handle. It's difficult to assess what other differences there are, if any. One may offer a different warranty, but at HD, for example, you can buy their 'lesser' quality version, and for about what you'd pay for the 'premium' one, you can buy an optional, add-on warranty to match it. Often, the difference in the WH is just the label they put on it when it comes to warranty (but not always ,a 'premium' one may have a bigger or a second sacrificial anode).
Tough call...if you're lucky, someone that knows will respond, but in general, they are probably equivalent.