Process Mapping - is a diagrammatic representation of the flow of information and/or material in a process. It depicts all the process steps and the decisions taken in the process. Flowchart is the most common form of a process map.
Swim Lane Mapping - is a type of process map which is useful when the process spans across multiple teams / departments / units. Each swim lane represents one department and steps done by that department are captured in its lane. This helps in clearly identifying the doer of the step and also helps in identifying the handoffs in the process. The lanes may be arranged horizontally or vertically.
Value Stream Map (VSM) - is used to understand the flow of materials and information through the value stream to produce a product or service to a customer. A value stream map tends to be a macro-level map and contains much more information at each step than in a normal process map (e.g. wait time, cycle time, inventory, quality, number of people etc.). It is commonly used to analyse the current state to identify opportunities for improvement and thereafter designing the future state of a process.
An application oriented question on the topic along with responses can be seen below. The best answer was provided by Arunesh Ramalingam on 9th October 2017.