Business Process

A business process is a

sequence of activities which produces an output such as a service or product.

A value stream is a:

represent the series of steps that an organization uses to implement Solutions that provide a continuous flow of value to a customer -- Scaled Agile Framework"

Both value streams and business processes can be modeled using mapping techniques e.g Value Stream Mapping (VSM) or Business Process Mapping (BPM). However, there are several differences between VSM and BPM:

Value Stream Mapping

Business Process Mapping

Origin

Value stream mapping became popular with the rise of Lean after world war 2

Techniques to model business process such as the flow chart, functional flow block diagram, control flow diagram, Gantt chart, PERT diagram, and IDEF have emerged since the beginning of the 20th century --Wikipedia

Purpose

Original purpose was to visualize the flow of goods from supplier to customer. As such more suitable to develop senior management insight for decision-making

More accurate and focused improvements in downstream activities

Scope

Provides a broader view of the organizational processes (360 view or big-picture). More high-level and abstract

Provides a more detailed view of organizational processes (deep dive)

Application

Used by business architects along with business capability mapping

Used by process architects to improve organizational processes