Hi, can anyone explain me the differences between them, please? Thanks a lot..
Blur will blur every pixel, regardless of the position on the screen. Depth of Field, on the other hand, takes into account depth information (how far is the object away from the camera). Pixels from objects that are "in focus" will get blurred less than pixels from objects which are "out of focus". So DoF is an effect that tries to add realism while blur just blurs ;-)
As Jashan points out, DOF varies the blur based on focus distance, where a blur filter applies uniform blur to the whole screen. DOF aims to simulate camera or eye focus where near and far objects are blurred out, keeping the objects in between in focus.
This page has some noticable DOF effect on the first image. The comparison shown there is without DOF and with DOF. It doesn't show blur, though. Blur is, again, "fullscreen blur".