Project management techniques and methods are going to be a big help, however product management bears more similarity with programme management, generally the following things are going to be expected from a product manager to a larger degree than from a project manager:

• Stronger involvement in the company strategy formation.
• Product strategy formation.
• Management of full product life cycle from conception to retirement: initiation, planning and monitoring of a series of projects to advance a product from one stage to another.
• Good understanding of and collaboration with marketing and sales: pricing, sales forecasts, sales support, understanding of user requirements and position on the market and so on.
• Participation in logistics: stock control, procurement, delivery etc.
• Deeper involvement with financial planning.

Some would argue, and I do disagree, that for a project manager specific domain expertise is secondary to a firm grasp of project management techniques. On the other hand a successful product manager has to know the domain and the product inside out. They are ultimately responsible for conceptual integrity of the product and all adjacent areas: from conception, manufacturing and logistics to “customer journey” and pricing.

There is one area where I have seen project managers fall short when dealing with product management: managing the maintenance aspect of product management.

But besides that, I think you are right, most of the expirience from project management is applicable in product mangement (I assume that you are talking about an IT product)

Project Management experience is definitely helpful in Product management as well. I don't see much of difference in expectations from both of aspects, it is the output that is important in both.

But there is basic difference which make their job different as below:

Project managers are responsible for the successful delivery of a project, a one-time endeavor with a goal, scope, deadline, budget, and other constraints. A project manager will work to align resources, manage issues and risks, and basically coordinate all of the various elements necessary to complete the project. When the project is complete, the project manager will usually move to a new project, which may be related to a different product.

Product managers are responsible for the overall and ongoing success of a product. Once the project to build the product is complete and the project manager has moved on, the product manager remains to manage the product through the entire lifecycle. Other projects related to the product may be initiated, with the product manager being the one constant stream throughout, defining the project goals and guiding the team to accomplish the business objectives that have been defined.

Product manager is some one who owns the product from initiation to scrapping of the product and project managers will come and go to achieve one or more objectives during this lifecycle of the product.

I would say that project management experience is helpful just a bit in transition to product management. If you go this path you will know all about requirements management, scope creep and iron triangle which will help you to set reasonable goals against project team.

But as a project manager you won't learn the most important product management thing - driving a product.

Project management is about getting things done but deciding what kind of things isn't a part of the job. Project manager has stakeholders and sponsors all around who decide what exactly should be done in the project. Project manager almost never adds something from themselves since that would just make project even more difficult. The goal is to possibly satisfy most of stakeholders (or the most important ones) and keep the thing within external constraints (budget, time).

Contrary to this product managers should generate a lot of stuff to add to their product. Possibly as much as possible but not more than it would blow the project up. Product managers doesn't try to find compromise between all stakeholders - they try to get all features for their product.

This isn't just about a mindset change. This is about working most of the time on a thing you've never worked before. Potential clients and future users were never a concern of project manager while they are (or should be) main concern of every product manager.

You can do one test: take your wanna be product manager hut and try to create a concept of a product which you wouldn't totally run down as incomplete and not-well-thought while wearing your project manager hut.

I think Product Management shares more in common with running a business than with running a project. See Can a Project Manager also be a good business owner and Is Project Management Strategic?

I think the strategic duties that a Product Manager must perform are not part of a Project Manager's job.