Besides the packaging and the fact that the ammo is loose,

I typically see three types of M855 for sale:

White box Winchester packaged
Brown box Winchester packaged
Brown box/can Winchester loose
Brown box/can Lake City/Winchester loose

Are all of these the same thing in terms of who and where it is manufactured?

Lake City has always been the most consistent and reliable ammo for me but I'd like to put a case in storage and wouldn't prefer to get the packaged white box since it's a bit cleaner as long as it is the same ammo.

All the exact same stuff, loaded to the same spec.  All Lake City.  Buy whichever you prefer with confidence.

AFAIK Winchester still loads 5.56 at their Oxford, MS plant, so it's not necessarily all the same stuff.

The headstamps and lot number prefixes will tell the story. I'd expect the white box stuff to be Oxford manufactured with WMA headstamp.

Confirmed with vendor - hollowpoint is correct

But you are also correct that there is a specific ammo that Winchester still makes in MS. These specific ones are all Lake City.

The white box stuff I’ve got is all LC manufacture

In the past before Winchester took over LC, The loose in box inside a bag (or Not) was the worst looking, tarnished brass, Paint flaking on green tips, little or no primer sealer and dents and dings, Shot fine but ugly.
As the packaging improved the better the ammo looked, up the best, stripper clips, bandoleers, and finally in cans correctly marked. Not sure about Winchester, didn't have consistent results back before they took over LC. Velocities had a wide spread and group size was not on par in my rifles.
Again, have not been involved with Winchester since it took over LC.

Agreed.

The loose Lake City stuff looks absolutely terrible but I've never had an issue with the ammo.