How many agencies have you ever heard of with "Defence/Defense" in their name have you seen that aren't military? How many organisations built for aerospace? There is a reason NASA and ESA are civilian operations, but the RAF and USAF/RCAF have Defence for their operations in sub-orbital and space operations.
SPD was gendarmerie. Military police.
Terra Venture was under the operations of the GSA, who had a severing military force for logistics, operations, combat (which you saw training in a military test field in the first episode), and research.