You may work for a company that uses titles as rewards or tries to be creative or funny with titles. For some, your title may not accurately reflect your job duties. Another problem is that the company where you want to work calls your job by a different name. Yet another problem is when you want a new job that’s a subset of your current job.
All of this leaves you with the wrong title for the new job. How can you get their attention?
Do away with the titles completely and use roles. If you are asked about your title, there is no need to lie. You can simply say that since titles often don’t mean the same from company to company, you chose to focus on your role.
If you still don’t like the idea, then do use your title, but underneath it, segregate your bullets into groupings headed by the role you played. Order your roles according to the job opening, not the order in which you did them at work.