I have seen positions such as Value Assurance manager. How it differs from Project Assurance manager or even Project Manager?
Whenever you find a job title that's not very common, it usually means that the company tried to put a name on some job responsibilities that are wider than what existing job titles can cover, like Project Manager for example. The job title usually also sounds cool and implies a certain degree of authority.
You can't really know what it means until you read the job description and see what one is expected to do on a daily basis. Other companies might use the same job title to mean a different set of requirements and responsibilities.
Every time I've encountered roles like these it usually meant some sort of Project Management Officer mixed with some Agile coaching and with a certain authority given by top management. Their job is to supervise projects within the company and make sure they all align for best results, or should I say "best value" in the context of this answer.
The authority given to such managers usually falls in the "Controlling" type of PMOs, which means that they don't take charge of projects (i.e. not "Directive") but when they say you should do something, you must do it, you can't ignore them (i.e. they are not just "Supportive").
So really, it's important what the responsibilities are and what you are expected to do on the job. Job titles matter less.