Hi. I am soo confused eith this whole thing. First of all: what the fluff is this? DMG says that effect needs to effect at least half of the sqare while Xanathar text says that a sqare needs only partly to be covered with a template to be in the area of effect. It seems like Xanathar says something that is canceling what is written in the DMG (or i am just stupied) 

Second. Is there any difference in using circule and using template that looks like a bunch of sqares in determining what fireball affects? I see difference in how the second variat works in diffrent pictures from Pinterest. I would like to show you one of them but I cannot post photos from my fone

The DMG is the "standard" ruleset and presents how a DM should interpret the Area of Effect.  

Xanathar's is "optional" or "alternate" strategies for conducting the game, so there will be some conflict in places.

Basically, you choose whether to use the Xanathar's template rules or the DMG standard rules, not both.

Edit:  Also, the rule for 1/2 coverage only applies to circular effects (spheres and cylinders)

The "squares" method you mention is the "token" method from Xanathars and is a second alternate way to determine Areas of Effect.  In it, instead of a 20' circle, you make a 20' square to show the area.

So, to recap, you can use either the DMG, the Xanathar's Template, or the Xanathar's Token methods, but only one at a time, not all at once.  Id recommend picking just one to use for your whole campaign or encounter so you are being fair to your players.

And if I recall correctly correctly, the DMG’s “half the square” rule technically only applies to “circular” (Sphere/Cylinder) AoEs, not any of the others.

There is definitely a difference in spell effects depending on how those effects are adjudicated to affect a grid. The method you choose is less important than the consistency with which you apply it.

Quote from iconarising >>

The DMG is the "standard" ruleset and presents how a DM should interpret the Area of Effect.  

Xanathar's is "optional" or "alternate" strategies for conducting the game, so there will be some conflict in places.

Basically, you choose whether to use the Xanathar's template rules or the DMG standard rules, not both.

Edit:  Also, the rule for 1/2 coverage only applies to circular effects (spheres and cylinders)

The "squares" method you mention is the "token" method from Xanathars and is a second alternate way to determine Areas of Effect.  In it, instead of a 20' circle, you make a 20' square to show the area.

So, to recap, you can use either the DMG, the Xanathar's Template, or the Xanathar's Token methods, but only one at a time, not all at once.  Id recommend picking just one to use for your whole campaign or encounter so you are being fair to your players.

 Oh ok then. Thanks for giving this explanation coz it was really strange for me