What is the difference between a director and senior director of product marketing?

This answer is going to be different depending on your company and its job levels, expectations, etc. So I can't answer it generically, but I can tell you what changed for me: the team size and scope of work.

As a director, I started out with zero direct reports and owned one product. My role then grew to be a team of 3-4 people and I owned a growing line of business. As a senior director, I've had anywhere from 4-12 people on my team, and the scope of work just keeps growing. But if you look at other directors and senior directors in the org, their stories are different, so this is just my experience.

Ask your manager for clear expectations and the difference between director and senior director. It will likely be a mix of team size, scope of work, executive communication, maybe P&L ownership or revenue targets.