Product managers may work with shorter term stakeholders on more fleeting initiatives, and they can also have longer term stakeholders. What's the difference?
Really not much. With longer-term stakeholders, typically you'll become better versed in their day-to-day life or work. You end up forming a relationship with them and building trust. You can start to predict their needs because you know them so well.
That trust helps considerably when there is bad news to deliver, because they know you have their best interest at heart.
There's no significant difference in how you approach short vs. long term stakeholders; you still need to communicate effectively with them and form some sort of rapport. The real difference is in the relationship and how well you can get to know them; developing and sustaining customer and stakeholder relationships is a key product management skill.