The source is directly related to the rewards gained by playing an activity or set of activities. This currently includes Quests and other action in-game.
This source is a custom aggregation of items that can be earned in many ways, but that share some other property in common that is useful to share. For instance, in Destiny 1 we would make "Reward Sources" for every game expansion: that way, you could search reward sources to see what items became available with any given Expansion.
The source doesn't fit well into any of the other types.
This source is directly related to items that Vendors sell.
BNet's custom categorization of reward sources. We took a look at the existing ways that items could be spawned, and tried to make high-level categorizations of them. This needs to be re-evaluated for Destiny 2.