What is the difference between first angle and third angle projections in engg drawings?

Third Angle Projection: The plane of projection lies in between observer and object.

                                           The object is imagined to be in third quadrant.

First  Angle Projection: The object lies in between observer and plane of projection..

                                           The object is imagined to be in first quadrant.

In first angle projection, that object is assumed to be in the first quadrant. Hence, the top view is projected below, i.e. to the x-z plane - which lies below the object. Hence when all the three view are drawn, you will get the top view below the front view. In the third angle projection, the object is assumed to be in the second quadrant. Hence when the entire drawing is finished, the top view remains on the top. 

Generally, these differences do rarely come in the industry as the drawings need to be so detailed and meticulous that entire plan(top view) takes one sheet and the elevation(front view) takes another.