These notions are by some used interchangeably. But I think that the ratio is just the calculation for instance W/H, BMI etc.Subsequently the outcome of this calculation can be used as an index indicating something: for instance BMI for obesity, waist circumferance or weight circumference/ length for risk of metabolic syndrome etc. It "indicates" something.
A ratio is just one number divided by another number (quotient). But.... this ratio can be used as an index of something else. See earlier remark. One could also name it an indicator. In Latin one meaning of index indeed is indicator.