Do pure and dry hydrogen are the same? What does dry hydrogen actually means. And what does pure hydrogen means.
It depends what you (or your field) is considering what an impurity is for a given substance. For example, if you want really pure methane, ethane will became an impurity. However, if you want gaseous alkane(s), there is no real difference between methane and ethane, so ethane is no longer an impurity.
On the other side, moisture can be your enemy, so pure methane (without ethane) can be considered bad if it contains 3% water whereas a mixture of methane and ethane (50/50) could be considered better because it contains only 0.1% water.
In your case, "pure hydrogen" would mean that "it is composed almost entirely of hydrogen gas" (but it can contain water) whereas "dry hydrogen" would rather mean that the gas does not contain water (but it can contain other molecules as well, but not too much)