The simple answer is: the Vector2 positions the sprite at the X,Y coordinates, while Destination rectangle fills the sprite to fit that rectangle.
More advanced answer:
Sprites are in reality quads made up of two triangles, since underneath all this graphics stuff 3D routines are used. So both Draw methods transfer the sprite to a quad. This quad is basically a rectangle.
So what the Vector2 variant does is create a DestinationRectangle internally like this when calling SpriteBatch.Draw():
destrect = new Rectangle((int)V2.X, (int)V2.Y, Texture.Width, Texture.Height);