Can an Indian student use the same SOP for two similar public policy programs at the same university, and how much does it need to change?

The core of the SOP, your personal story, your background, your values and long-term goals, does not change between applications to similar programs at the same university. You are the same person. What changes is the emphasis: which aspects of the program you are highlighting, which faculty you are referencing, and how you frame the specific fit between your goals and that particular course's strengths and focus areas. A useful way to think about it is that the opening and closing of the SOP can be adapted with relatively minor changes, while the middle section, where you describe why this specific program is the right next step, needs to be rewritten for each course.

• Admissions committees for different programs within the same university are not typically coordinating their reads to check for overlap, but a generic SOP that could apply to any program anywhere reads differently than one that demonstrates genuine research and clear fit.
• Spending an hour to tailor the program-specific sections is worth doing because it signals that you chose this program deliberately, which is what US and European admissions processes reward.