A downstream design uses a poppet that will open to vent excess intermediate air pressure. An upstream design will not vent this excess pressure and some other form of over pressure relief must be used.
In practice, if the first stage high pressure seat fails, the first stage intermediate pressure will rise and could cause a failure of the low pressure hose leading to the second stage unless the excess pressure vents through a downstream second stage or an over pressure relief valve.
Becuase of this threat, the term normally is applied to second stages although there are also up and downstream first stages. In fact all diaphragm first stages use an upstream design where the seat carrier is located on the upstream side of the high pressure orifice in the first stage. But it does not really matter as if the poppet fails closed, the pressure will still be contained by the regulator as it is rated to greater than the full tank pressure anyway.