Ralph, the reason Kenmore washers were so different from the Whirlpool models of the time was because the majority of Whilpool's production was for Sears. Also, at one time Sears owned over half of Whirlpool Corp. stock. The same was true for Roper and some of their other suppliers.
As far as Oster is concerned, I'm sure the majority of their production was sold under the Osterizer brand, rather than a private label such as Sears. It would probably have not been very cost effective to make many changes for the Kenmore version.