Complex question and no single answer fits that same question for all products.
With NewEgg products, first I check the DETAILS and see if one is Retail Box, Comes With Software, With Any Cables, etc.
No? (And in this case, no - it seems both units will be packaged the same, although one may come in a Retail Box, and one will not - the OEM won't, probably - it may come in simple bubblewrap.)
Often "OEM" indicates "Our manufacturer made their model number and then ran the factory for days longer, produced 10,000 extra units that we shipped to other brands that will relabel them as their own."
So you might get a Drive (or a product) that was made by Factory XYZ but will have a Sony label on it, while the XYZ Brand has their own. Identical drives, different logos.
Sometimes, OEM products can be updated more easily, and sometimes, with much greater difficulty.
MyCE is a favorite site of mine because, often, I'll see these very explanations here. "This version of that drive allows better firmware updates, the OEM version doesn't." Or vice versa.
The LG BH product, in this case, will probably have firmware updates only available thru LG. The LG OEM unit (WH...) might have firmware ujpdates made available thru other sources.
This means, "Sounds like more research!"