I live in a country in which it is possible to hear both Sunni and Shia (azan), I noticed that Sunni azan always precedes Shia azan by few minutes ( from 5 to 15 min).
Why is there such a difference?
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The logic behind this is that:
if azan is recited before time it will be invalid.
And if it is recited after due time it is valid.
So shia recite azan just after few minutes the calculated time to make sure it will be valid. As nobody can precisely calculate the actual prayer time.
Different sects have different calculation methods. The sole difference is the angle: http://praytimes.org/calculation/
In this website you can see all of them. In my opinion, whoever takes whichever, is fine as long as their intent is to just follow God's order for doing the prayers.
They have different calculations for all the prayer times. They even PRAY in another manner. For example, Sunnis pray two to three minutes after the sun is completely below the horizon, but Shias don't offer Maghrib salat until all bright warm colours, or redness in general, have disappeared. It's a matter of who learned what from which schooling.