Both calibers are based on a necked down 30-06.
Close, but not quite, tho I may be splitting hairs on this one.
From the info I've found, both the 30-06, and the .270 "cartridges" (not calibers) were based off of the 30-03 cartridge. I guess that since the 06 was developed about 20 years sooner one could surmise that the .270 was developed from the 06, but in fact both were based off of the 30-03.
You are correct about the 25-06 being a necked down 30-06 cartridge that was considered to be a wildcat until it became standardized by Remington in 1969. That said, all were developed from the original 30-03 platform.