Thanks R0J0hound for pointing out difference.
But difference beatween what is overlaping at offset in CC and C2 is exactly that what leads to some problems in case you would like to make built-in platform behavior work "perfect" with smal sprites: to prevent sinking, penetrating sprites in obstacles for 1-3px.
Why is that so:
As I understand it, collision happens when sprite is on obstacle and it functions like triger. On the other hand 'overlaping at offset' in C2 funcions exactly the same as collision(=overlaping 1px), but not as triger, more like while: 'overlaping at offset 1' is basically equal to while it's coliding - if sprite rectancle is the same size of the collsion box.
If solution to this is that you make collision rectangle smaller one px from sprite size, and then if sprite with platform behavior due to not working accuratly with small sprites sinks in ground, and you then set its position so that is visibly on obstacele (set SpriteY to Obstacle.Y-obstacle.Height/2-sprite.Height/2) it is not colliding whit it so you can't jump.
If you make it collide so it can jump you can't use overlapinng left or right(overlaping at offset 1,0 or -1,0) becouse it is overlaping like colliding, standing on the line of obstacle...
Yet again I think that what counts for overlaping in CC is better, because in C2 it's overlaping at offset of 1 is basicly same as collision detection.