Does Paired T-Test provide the same result as Wilcoxon Signed Rank Test on the same dataset? In principle they are trying to test the differences in dependent data.
However, do they always provide the same outcome on the same dataset?
What happens if we get contradictory result by using both method on the same dataset?
 A: A paired test amounts to a one-sample test on differences.
For a small normal sample of differences D, the t test and Wilcoxon
signed rank test may give similar P-values. (For normal data, the Wilcoxon test has slightly less power to detect $\mu\ne 0.)$
set.seed(2022)
D = rnorm(20, 1, 1)   # population mean 0

summary(D)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-1.90063  0.04153  0.86726  0.72179  1.39584  2.01956 

stripchart(D, pch="|")


t.test(D)$p.val
[1] 0.004437353           # Significant at 1%
wilcox.test(D)$p.val
[1] 0.005580902           # Slightly larger P-val
                          #  Still signif at 1%

However, if the sample of differences has a far outlier,
then the two tests may give very different P-values.
set.seed(115)
D = c(rnorm(19, 1,1), 30) 

summary(D)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1867  0.8562  1.1614  2.5817  1.5485 30.0000 


t.test(D)$p.val
[1] 0.09067962           # Not signif at 5%
wilcox.test(D)$p.val
[1] 1.907349e-06         # P-val near 0; Highly signif,

Note: Ideally, the puzzle of making sense of contradictory
decisions from the two tests shouldn't arise. Before doing either test, you should
try to figure out which one best matches the data, perhaps by looking
at a histogram, boxplot, or normal probability plot. Doing both tests
and picking the one with the smaller P-value, would be 'P-hacking'
and could lead to 'false discovery' of a non-existent significant
difference.
