If you are interested in a graduate school where English is the primary language you will most likely be required to submit a GRE or GMAT score. However, you are often also required to submit an English language proficiency exam score like the TOEFL or IELTS.
All of these exams are in English; the major difference is that the GRE and GMAT include sections that test your quantitative (math) skills. The GRE and GMAT is a more challenging test when it comes to the level of English, since they have been designed for native speakers in mind.
A good English comprehension score on the GRE and GMAT can waive the need of submitting a TOEFL or IELTS score. Similar to what a good ACT and SAT score does for an undergraduate program.
Another example when submitting an English language proficiency exam score can be waived is if your Bachelor’s degree was completed in an English speaking country or program, for example if you’re originally from Brazil but studied in the U.K. for you Bachelor’s degree.
However, this may be contingent on whether you graduated from a Bachelor’s program or not. Another factor that will matter is what type of master’s degree you are pursuing.
The GMAT and GRE test your comprehension, analytical and quantitative skills. The IELTS and TOEFL only test the language skill that is required at a college level (reading, listening, speaking and writing).
If you are taking the TOEFL/IELTS and the GMAT/GRE, it’s a good idea to start with the TOEFL/IELTS exam as it may be beneficial in improving your English skills before taking the more challenging tests.