Are the two terms the same or not? In what sense Heidegger makes a distinction between the two?
Can someone give also simple examples of the difference?
The science that studies a be-ing is, for Heidegger, ontic [ontique], and it is necessary to distinguish it from the science of the being of a be-ing which alone is ontological [ontologique]. Let us examine these distinctions more closely. The attributes of a be-ing make it to be of this or that determination. In identifying its attributes, we say what it is, or end up at its essence [GT : the realm of the ontic]. But alongside the essence of a be-ing, we can affirm, through a perception or demonstration [GT : the realm of ontology], that it exists. (Emmanuel Levinas, 'Martin Heidegger and Ontology', Diacritics, Vol. 26, No. 1 (Spring, 1996), pp. 11-32 : 15.)
So, for example, I can take X, an object in my world, and determine its essence, fix its essential attributes. This is an ontic exercise. I can also consider what it is for X, with its essential attributes, to exist. In contrast this is an ontological inquiry.