It has to do with whether or not different groups of passengers will share passenger cabins. If the mission lists the passengers as a group such as "6 tourists", "11 scientists" or "5 refugees" then they will all happily share a single cabin (within capacity limits) but if the group is led by a passenger with a name such as Bren Thimbledome or suchlike, then that passenger's group will occupy an entire cabin no matter how much extra available room in the cabin. Also, if you do not have enough cabin capacity, missions that you do not have the cabin capacity to carry will not appear in the available missions list. o7
Pro-Tip: The various Mission Boards will never offer a cargo or passenger mission that your ship cannot complete at that moment but if you accept a mission and then purchase fuel you may find that your ship is now too massive (heavy) to make the jumps necessary to complete your mission(s). If buying fuel (i.e.: you have no fuel-scoop), always purchase fuel first thing on landing, before going to the mission boards.