This is a popular question on the AP exam for Micro. A lump sum tax is a total fixed cost an therefore will not impact the production decisions of a firm. On the other hand, a per unit tax is like a variable cost, and variable costs impact MC which impacts the output decisions of a firm. If the question asks for a lump sum tax or per unit tax they will usually ask you how this impacts deadweight loss. Lump sum taxes don't impact deadweight loss because it won't change production decisions. A per unit tax will decrease the deadweight loss by the tax. If the per unit tax is the external cost then it will remove the deadweight loss completely.
BTW, the distinction between these taxes is also commonly tested in the PC, Monop, Monop Comp, etc market models. Make sure you practice this concept.