They are NOT the same.
You can transform a residual dividing it by the square root of the
expected value. This produces the standardized residual, also
called Pearson residual. In turn, a Pearson residual can be divided by
the standard deviation of all residuals, thus obtaining the adjusted
residual.
The great usefulness of adjusted residuals is that they are standardized
values, so it is legitimate to compare residuals from different cells.
Furthermore, adjusted residuals follow a standard normal frequency
distribution (with mean zero and standard deviation one), so we can use
a computer program or a probabilities table to come up with the
probability that a certain residual’s value is not due to chance. In a
normal distribution, 95% of the values are roughly within the mean plus
or minus two standard deviations. So, if the adjusted residual’s value
is greater than two or lesser than minus two, the probability that this
value is due to chance will be less than 5% and we’ll be able to say
that the residual is significant
Adjusted residuals allow us to assess the significance in each cell but,
if we want to know if there’s a global association between variables we
have to sum up all adjusted residuals. This is because the sum of
adjusted residuals also follow a frequency distribution, but this time
it’s a chi-square frequency distribution with (rows-1) x (columns-1)
degrees of freedom.
As far as I know, ADJUSTED residuals were introduced and recommended
by Shelby J. Haberman in or around 1972 (and thereafter),
but they have been recommended by many others over the years.
Look at contingency table literature for examples.
The list of possible references is exceedingly long.
Haberman is still an active contributor to this literature (now at ETS).
Cites to Haberman's early work might include
1970: The general log-linear model. Shelby J. Haberman.
Ph.D. Dissertation, Univerity of chicago.
1972: Algorithm AS 51: Log-Linear Fit for Contingency Tables, S. J. Haberman
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 21, No. 2 (1972), pp. 218-225
1974: The Analysis of Frequency Data. by Shelby J. Haberman;
Chicago: University of Chicago Press.
... Mark Miller