In audit verbs count a lot.
though review and check have nearly same meaning there is difference in how it is used.
We know audit itslef means check. Its better to see how it is used. E.g. review of audit/accounting policies/procedures - (review of procurement policies - means new policies will replace the existing or not) however Check audit policies are complied means go through list make sure they are followed. Often where there is check we know the end result are known.
This is my personal understanding and English is not my first language. So, ...
Same thing really, to look over or check/review something!!!
Review in my own understanding means to look through an already performed work in search of evidence. While check is to look at a particular item in a work done to know if it was done accurately.