More context from the docs, looking at the arguments to
method: character string specifying how genes and contrasts are to be combined in the
multiple testing scheme. Choices are "separate", "global", "hierarchical"
adjust.method: character string specifying p-value adjustment method. Possible values are "none",
"BH", "fdr" (equivalent to "BH"), "BY" and "holm". See p.adjust for details.
These are two different options.
One option (
adjust.method) chooses the multiple test correction, for which the default is BH/FDR.
The other option (
method) decides how the multiple test correction is applied, for example can it be applied separately to different genes or across contrasts.
method = global in this context just means that every single test statistic is considered at the same time. An alternative to this would be to consider a nested design.
method = separate applies the correction to each column of your matrix independently, such that in a $m x n$ matrix of statistics, the "number of tests" is $m*n$ for
global and $m$ for
For understanding the effect of the number of tests on FDR, I suggest consulting the FDR wiki page. Basically, using a
method other than
global will increase power.