So, if a Wizard has, for example, only the third mental stress box available (☑️☑️☐☐) and Conviction 4, will any Evocation Spell with 1 to 6 shifts cost him the same?
It costs 1 plus the number of shifts of power, minus the conviction, with a minimum of 1. So 6 shifts of power costs 3 stress so the 3 box is ticked off, and 4 costs 1 stress which rolls up to the first available box (also the 3 box).
Or are there different rules for Evocation Mental stress?
No, it works just like any other kind of stress: a lot of small bits of stress can add up, but one big bit of stress makes the small stress pale in comparison. Wizards, in the Dresdenverse, are powerful beings and flinging around a few spells per scene is easy for them. It's when they are forced to cast spell after spell after spell or when they conjure a great work that things get tough.