As you yourself have pretty much surmized, you don't shoot a 35 Whelen in a 35 Remington. The two cartridges are completely different.

The 35 Whelen is based off the 30-06 case, necked up to 35 caliber and as such it throws heavier bullets better than the 06. It was a wildcat for many years until Remington started chambering for it. They chambered it in the 700, 7600 and I think the 7400, but I'm not sure about that one. It didn't do as well as they'd hoped and I'm not sure what they are chambering it in now.