Both IELTS or TOEFL are designed to test your proficiency with the English language, especially your ability to communicate effectively in a classroom setting and fit into a predominantly English-speaking culture. Consequently, while SAT/GRE/GMAT test your verbal ability, including reading comprehension, vocabulary, etc. IELTS vs TOEFL only test how comfortable you are with the English language. That doesn’t mean these tests are a cakewalk, but you won’t be stretched nearly as thin as with the SAT, GRET or GMAT.
IELTS or TOEFL is usually a requirement for students from countries where English is not the primary language. In some countries, taking either of these tests may also be required for obtaining a visa. At the same time, high scores in the standardized tests – SAT/GRE – or a English-heavy course curriculum at the high-school or Bachelor’s degree level (for students applying for Master’s and PhD’s abroad) may exempt you from these requirements, though this is the exception, not the norm. In 90% cases, you will be required to take either the IELTS or TOEFL.