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Two different things. A basis point is 1/100 of a percentage point. So is bond yields change from 3.50 percent to 3.55 percent the yield has risen 5 basis points.

The 'point' difference in the stock indexes refers to the simple difference between the index value at the end of each day. In your example the index ended the prior day at 11,436.92 plus 47.59 = 11,484.51.

Its movement during the day equals a 4.1% change. (47.59/11484.51)
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