Process modelling should be viewed from the point of view of a notation of business process management as one of the most widespread standards of process modeling. You can check definition of the notion here. At the same time it is obvious that there is a set of languages of modeling and various systems. But nevertheless BPMN is the already developed standard of process modeling, and therefore you should take it as a basis in the description.
Process from the point of view of a business model is the sequence of some events and actions which have the beginning and the end.
For example, functional modeling considers a business model from the point of view of an entrance and an exit (the available resources and desirable result). And this process it is based on the sequence of actions in certain borders, in case of BPMN it will be the beginning and the end of an event.
All processes can be decomposed (to be detailed) into subprocesses up to specification at the level of tasks, i.e. actions which further specification is impossible. Process is a certain sequence of actions which needs to be executed to receive a certain result. It should be noted that in business model as process the result can not be obvious in difference from functional model.
The fundamental difference of process modeling from functional is that at process modeling the main attention is paid not to what we want to receive, and what needs to be made for obtaining result, i.e. not to results of this or that activity, but the sequence of actions.
For example, in the course of specification of each function there is a transition from functional approach to process. I.e. generally, we consider model from the point of view of opportunities and desirable result and when we pass to decisions for each function, here obviously process approach, i.e. a step-by-step algorithm of actions for achievement of result already practices.
Imagine that in functional model there is “a black box”. And after decomposing we already consider it not as function and as process, and the sequence of actions at reception of the order is already process approach.
There is also one more very important difference. The functional model can’t be used at any realization or systems, only for design. And process approach allows to create the executed models, i.e. descriptions of the sequence of actions which we can translate further on some environment for creation of system of the collaboration of the enterprise based on process approach.