I was wondering if studying for GRE helps MCAT in anyway? How similar are verbal sections of GRE and MCAT?

Its been a long time since I took the GRE but from what I can remember about the GRE, the MCAT has been a whole different experience for me.

Might help you to talk to an instructor at Kaplan or Princeton Review. They tutor both under the same roof and some of their instructors tutor for multiple tests so they would be able to do a much better comparison.

Also you could compare the prep books at Barnes and Noble or your local bookstore.

Since I am just doing the research into Med Schools, what is a GRE?

GRE is the Graduate Record Exam. This is the test needed for a Masters and/or PhD

Other than helping you in your test taking skills, they are 2 very different tests. Preparing for the GRE does not help with the MCAT.