I'm asking you why they consider that Wilcoxon test and U Mann Whitney test are the same ? Can we use this test to examine 2 numeric variables for independent groups ?
You are right that both tests are nonparametric alternatives to the t-test for comparing 2 samples. However, Wilcoxon is designed to deal with DEPENDENT samples by comparing central tendencies of the samples (mean or median). Mann-Whitney-U is designed for INDEPENDENT samples and compares the distribution of your samples.
The Wilcoxon rank sum test and the Mann-Whitney test are equivalent. People often refer to this test as the Wilcoxon-Mann-Whitney test to avoid confusion and to share the credit.
The test for paired samples is the Wilcoxon signed-rank test, and is different.
However, in R, both tests are performed with the wilcox.test function, by choosing different options. Another option are the wilcox_test and wilcoxsign_test in the coin package.