Don't always assume that Ancestry.com and FamilySearch are using the "same index." The indexes to the same materials could have been created separately. They do NOT share indexes.
A good example of this was a search I recently conducted for Joshua Sledd in the 1852 California Census
The California 1852 State Census at Ancestry.com transcribed his last name as Stedd--as shown in the image below:
FamilySearch indexed the name as Sledd as shown:
It is easy to see how the name was read in both ways when one sees the image.
And the whole reason for the post?
I found Joshua in the 1852 Census index on FamilySearch--which does not have the images.