Directivity and gain are similar the main difference is losses (efficiency of antenna )

Gain = eff*Directivity

also Gain and directivity are functions of Theta , so you have a function not certain unique value ,

Gmax or Dmax is the Max. value of the function of D(Theta),G(theta)

thank you for your reply sir,

what about gain and directivity Vs frequency? can i find my max gain of an antenna from the frequency?

of course because in the HFSS tree you define the curve or the results table you want. you define the abscisses and the ordonnees.

Thank you sir