You ask a really good question! Here are some of the similarities between the GMAT and GRE.
QuantThe good news is that the actual quant topics, such as linear and quadratic equations, roots and exponents, number properties, inequalities and absolute values, functions and sequences, probability and combinatorics, ratios and percents, rates and work, unit conversions, general number skills, estimation, statistics and overlapping sets, and geometry, for example, are tested on both the GMAT and the GRE.
That being said, you’ll have to familiarize yourself with answering Quantitative Comparison, Multiple Answer, and Numeric Entry questions (these types of questions are not tested on the GMAT.). You can find a few examples here:
https://gre.targettestprep.com/gre-quant-examplesVerbalUnfortunately, there is less carryover from GMAT verbal to GRE verbal. Both the GMAT and GRE test Reading Comprehension and Critical Reasoning; however, on the GRE, Critical Reasoning is referred to as “single-paragraph Reading Comprehension.” That being said, one major difference between the verbal sections of the GRE and GMAT is that the GRE focuses on vocabulary (within Text Completion and Sentence Equivalence questions) and the GMAT focuses on grammar (within Sentence Correction questions). Although you may have mastered GMAT verbal, if you find that your vocabulary skills are lacking, you may have some trouble with GRE verbal.
While these are just a few points, you also may find it helpful to read the following articles:
GMAT or GRE, which one should you take?How to Score 330+ on the GRE — A Guide for SuccessGood luck!