The short answer
Many Indian startups flip to a US holding company, so your options may be over foreign shares even though you sit in India. That mostly changes the paperwork and the tax detail, not the basic idea. You will likely deal with a US style plan (often RSUs or options over Delaware shares), a strike or vest value set in dollars, and currency risk between grant and sale. When you sell, gains are generally taxable in India as your resident income, foreign shares must be reported in your Indian return, and you may face US withholding or filing too, with relief under the double tax treaty. Moving money in or out runs through India's foreign exchange rules. This is genuinely more complex than a domestic grant, and the rules on foreign asset reporting and treaty relief change, so work with a CA who handles cross border equity before you exercise or sell.
A curated summary to orient you, not advice. The resources below are the real value.