Just read the Taylor rule and the formula in the note stated as:
 r(target)=r(netural)+0.5(GDP expected  GDP trend)+0.5(expected inflation rate  target inflation rate)
Then, I opened my CFA level 2 note and found a Taylor formula to forecast exchange rate below:
 R= r(neutral)+ Pi + Alpha*(PiPi*)+ Beta *(yy*)
Are these formulas the same? If so,

Why would the first formula’s alpha and beta set to 0.5 by default?

Why would the second formula has an additional Pi (inflation) added to the neutral rate?
Thank you!