Due to the naming scheme of S3’s generic class, both functions are similar to one another. However, they are not related to each other.
t.test() performs t-test and is generic in nature.
t.data.frame() is called by the generic t() for transposing the input data.
As a result of S3 dispatch rules, t.test() along with t() would get called when the latter is applied to the class “test”