Short answer :
Long answer :
Dual Stand By: It simply means that your mobile will be in connection with both mobile service providers at the same time and you can either place or receive a call on either of the mobile numbers. But, as you are busy with one number, the other number goes "Not reachable"
Dual Active: Your calling party will never hear "Not reachable" message if he calls you on second mobile number when you are busy on talking on first number. He will be just on "waiting" that time ....
Reason: Dual Active mobiles use TWO processors to handle both SIM where Dual Stand By mobiles uses only ONE processor to handle both SIM