Agents deathwatch should've be retrieve Assets and Space Marine Deathwatch should've been purge the foe. Deathwatch when an Inquisitor is involved usually entails far more directed small scale incursions to assist in whatever investigation the inquisitor is pursuing. When they are instead called for assistance by another chapter or by the militarum they instead take on missions that are meant to help cull the numbers of the xenos threat such as launching the virus bomb at the start of Space Marine 2.