It's a rather blurry distinction between the two, and they're often used interchangeably. Appraisal is usually used in the sense of "evaluation" or more broadly determining how much something is worth and how good it is, while review usually implies making sure something meets some particular standards and trying to find areas for improvement.
But it's not a hard rule, and in many contexts those definitions will either overlap (eg. a performance review of an employee and a performance appraisal are essentially the same thing), or one of them will be idiomatic (eg. you'd always review, not appraise a movie).
In your case, while review is probably the more precise word to use, your boss might prefer appraisal because it has more positive connotations. As an employee, I'd be more scared of a performance review than a performance appraisal - I associate reviews with making sure I meet expectations and standards, and appraisals with determining how much value I bring.
If you want a more precise (and more terrifying) word, I'd consider audit - this makes it very clear that the authority is formally verifying that you're meeting its particular set of standards for the license.
And, of course, it's possible that there's already an established, specific legal term (or an official English translation of it) for the exact process you're going through, in which case you should use it.
