Most interviews these days are behavioural or competency based.
Interviewers ask questions to elicit how candidates have demonstrated particular skills in their current and recent roles rather than focusing on specific knowledge or expertise (within reason).
First I would list all the current skills or capabilities that are required of your current role and do the same for the new role. If you have one look at the job descriptions or the internal advertisements.
Then, think of 2 to 3 recent examples of where you needed to demonstrate that capability. Think of the situation, what did you do and why, what were the challenges, how did you overcome them, what was the result, in hindsight would you have done something differently and why, what did you learn.
Where there are skills in the new role that are not in the existing role – then you will need to get creative with interpreting your achievements – but I am of the view that if you are missing a particular skill then be honest it can be learnt in the right environment.
IMO the term project management is pretty vague.