Naturally, you should start by investigating the content of the GRE for yourself. There are definitely plenty of elements in common, but there are numerous differences, as well. Here are some examples of what GRE verbal questions look like:
https://www.ets.org/gre/revised_general ... _reasoning You might notice that the GRE looks a bit like the new IR section on the GMAT--it uses a mix of question types, including questions with more than one correct answer. More importantly, the GRE is very vocabulary-dependent, as evidenced by the text completion/sentence equivalence questions, which are unlike anything on the GMAT.
On the quant side, the range of content is fairly similar to the material on the GMAT (at a somewhat lower level), but again, the test format is again quite different.
If your GMAT instructor feels confident in their ability to handle this material, that's fine, but you shouldn't simply prepare as if you will be taking the GMAT. You will definitely want to work with GRE-specific materials. If this tutor is not up to that challenge, you should find another one.