A friend has asked to me to find out why there are two different calibres under this same denomination, .360 NE 2-1/4, ie. .358 and .366. Any information out there?

Standardization as we know and expect it today did not exist back in the .360 2-1/4" days, particularly with cartridges that started off as black powder rounds and later were 'transformed' into nitro rounds. It would not surprise me to find rifles chambered for the .360 2-1/4" that would measure from as small as .358" all the way to .366" and even larger. Just as with most old German rifles, the only way to be sure is slug the barrel and make a chamber cast.