Paul is in the executing process, while she is in the initiating process.
There are five stages of project management: initiation, planning, execution, performance (or monitoring) and project close.
The Initiating Process is the first stage of the project where you will figure out whether the project is conceivable and should be undertaken. Thus, when she calculates the funds available in their budget, she is in the initiating process.
The executing process is the third stage of the project life cycle. It involves coordinating people and resources, integrating and performing the tasks according to what was determined previously in the planning project phase. Thus, Paul is in the executing process when he contacts potential suppliers to ask for price quotes.