Unfortunately, there appears to be no agreement amongst the checklist sites as to what to call them. Some pages say Brown vs. Orange, some say Natural vs. Orange, some say Solid vs. Orange, others say Left Ear Showing vs. Left Ear Not Showing. Some call one variation "version A" and the other "version B", while other pages do the opposite. We've even seen auctions on eBay claiming three variations of the same card, which is not reflected by any of the online checklists.
We have decided to use the nomenclature on the PSA checklist. They tend to call the "Brown Background" variations version B and the "Orange Background" version A (except for card #257 for which they call the "Orange" version A and B is called "Dark Pale"). Auctions on eBay seem to be mixed, with a majority calling the Orange "versions A" and Brown "versions B" in contrast to the PSA list.
All of the Baseball/Wacky Error cards, for which the non-Wacky versions come in both Orange and Brown variations, that we've obtained scans of, have been the Orange version (version B according to the PSA checklist). Therefore, we are assuming the ones we have not seen scans of are also version B (as denoted by the PSA checklist). But until we see scans of them all, we cannot be 100% sure. If you have more info or scans to share, please let us know at firstname.lastname@example.org.