UPDATE with JOIN on 100mm records, how to do this better? (in T-SQL)
I would take a different approach.

Instead of updating existing tables, just build a new  table that has what you need in it.

This will almost certainly be faster:

SELECT DISTINCT
    AutoClassID,
    &lt;Other fields&gt;
INTO
    AutoDataImportStaging.dbo.Automobile
FROM
    AutoData.dbo.AutoClass


As currently written, there are a lot of logical operations happening:  


Read all values of A.AutoClassName
Read all values of B.AutoClassName
Compare A and B values
Of the matching set, read all values of B.AutoClassID
Update existing values of A.AutoClassId to be the B.AutoClassId value through whatever indexes exist