One of the root cause of this misunderstanding is a confusion between Flow-Of-Control (FOC) and Flow-Of-Assets (FOA). Note: assets maybe tangible (e.g. goods, products) and intangible (e.g. money, value, cost, information). Assets are more generic than resources.
Flow of assets
FOA is a coordination between different activities by sending to them and receiving from them some assets to transform. Process as FOA is executed as in illustration below. Activities are only activities for transformation of assets.
IDEF0 notation and many diagrams with exchange of data between various systems or components are typical FOA.
FOC is a coordination between different activities by sending to them and receiving from them a special marker (token). Activities are free to fetch some assets as inputs and deposit some assets as outputs. Thus, activities that do other “work” in addition to transforming inputs to outputs (e.g. monitoring) are explicitly coordinated as well.
Workflow notations and BPMN are examples of FOC.
Cooking is an example of FOC. For example, to prepare a Swiss raclette, it is mandatory to complete all the following activities: 1) turn on the heat and melt cheese, 2) fry onions, 3) boil potatoes, 4) brown bacon and 5) find pickles, at the same time (or just-in-time). Depending of the situation, one has to start different activities at different time and coordinate their cooking.
More complex cooking example is the serving of different dishes at the same time. The chef coordinates their preparation.
Business process in BPMN is explicitly-defined FOC.
FOC defines FOA which is implicit but easy to generate (or make explicit). At the same time, it is not possible to generate FOC from FOA.
Value-stream is FOA for assets which are related to value – cost, products, etc.
Value-stream is a view-point (projection) on the underlying end-to-end business processes (more correctly, a system of processes).
Another example of FOA is VDML.
Maybe related topic - http://en.wikipedia.org/wiki/Behavioral_modeling