No, no and no more. The version in no way describes the contents of the box, but the method of distribution.
The box is a product packed by the manufacturer, so to speak at the factory - that is, when it came off the production line, you have it at the time of purchase and you are covered by the manufacturer's warranty.
OEM - a licensed product, packed by an intermediary and you are covered by a store warranty, that is, it is serviced by, say, a computer, not an intel
The contents of the box may be poorer or richer in each version. OEM due to the fact that it is usually less attractive, due to the fact that it is only a license, not a direct manufacturer - it is often packaged in a poorer version to lower the price, but it is not the rule, it may as well be physically the same box that the manufacturer gave, and the only one with the broker's logo on it. It can also contain a lot more than the manufacturer has put in the factory ...
BULK - it is different here, because technically speaking, by definition, it is a product not prepared for sale - usually from an exhibition, often without factory packaging, often with a shorter warranty, and certainly always cheaper. For example, I bought a BR BULK drive, which was about 10% cheaper by about 10%, not so long ago - because it wasn't so much on display as it was part of a computer that sold without a drive to lower the price of the set. And in general, they even had a factory box in stock and I got a full 2-year warranty, as in the case of a regular box.
Oh - and BULK can be both OEM and boxed.