A common situation is that Product Managers or Project Managers (PMs) become Product Owners (POs), and it's more of a change of job title than a change of methodology. PMs are used to aiming for deadlines, often with a narrow view of what's important to have done by that deadline. POs aim to get the most important work, as measured by a business value calculation (BVC), done first. Deadlines become just another factor in the BVC, as often deadlines are self-imposed and a person who made a promise to a customer to secure a sale will just have to go back to that customer and apologise. (That potential loss of company reputation is another factor in the BVC, but let's not get side tracked.) That's not to say that deadlines aren't important, but some deadlines - e.g. an accountancy product needing to meet the requirements for tax legislation that's coming into force on a specific date - are much more important that others.
Similarly, the BVC acts as a black box for the type of work, so where a PM will focus on their specific project or user group need, a PO will treat legislative, statutory, customer requirement, project, bug fixing and technical debt work in exactly the same way. All types and pieces of work are measured using a BVC, and if fixing a piece of technical debt has more business value than a customer requirement or meeting a project deadline, then so be it - the technical debt gets done first.
This transition from deadlines and narrow views to business value and a holistic view is definitely difficult for some people to get their heads around, especially in companies that run dirty agile. If you, or someone you know, struggles to understand what, how, when and why a PO does what they do, then the video below is for you. It's only 15 minutes long but it's worth it no matter what your deadlines are: