information-ratio

I'm confused on which Information Ratio to use. It appears that there are two equations. This depends on active or residual? = Alpha / Tracking Error = Rp - Rb / Tracking Error

The information ratio is active (or residual) return divided by active (or residual) risk. Active risk is also called tracking error, so the "active information ratio" is given by (active return)/(tracking error). Alternatively, a more technical approach is to use alpha (aka, residual risk) so...

I show IR = alpha/volatility(alpha) and..... t-statistic = alpha coefficient/alpha s.d. How are these two different?