In 2x and 23 x is called index and 3 is called power or exponent why?

There is not much difference at all. However if you look closely

Index/ expoenent is the math word used to denote the number of times the digit is multiplied by itself. The word power is preceded by a digit or equation indicating the specific number of times it is multiplied by itself.

Note that the index/ exponent is not limited to digits but could be an equation (as you said 2^x), or other math functions including trignometric functions.