In XComLW_SoldierSkills.ini, it appears Trench Gun is referred to by values named "STREET_SWEEPER_*" while Street Sweeper has names "STREET_SWEEPER2_*". #2 has a longer cooldown and a greater cone AoE.
The mouseover text for Trench Gun says it has a cooldown of "three turns" but on line 225 of XComLW_SoldierSkills.ini it has:
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STREET_SWEEPER_COOLDOWN=4