I have heard people saying that brownies are simply a smaller version of chocolate cakes, is that so? If not, then what could be the differences between brownie and chocolate cake?
Brownies are denser then cakes in general. This is achieved through the different cooking methods and some slight differences in ingredients.
The main difference in ingredients is that chocolate cakes tend to get their chocolate flavour from cocoa powder, whereas brownies use melted chocolate (and possibly some cocoa powder). Melted chocolate gives a denser texture than cocoa powder.
Brownies tend to be prepared by simply melting the butter and chocolate, and stirring all the ingredients together. A chocolate cake tends to either cream the butter with sugar or whip the sugar and eggs until fluffy, and then just fold in the remaining ingredients. This adds air to the cake which the brownie lacks, leading to a cake that's less dense than the brownie.
All that said, chocolate flavoured baked goods come on a texture scale from really dense (a very fudgy brownie) to really fluffy (a chocolate angel food cake). Many recipes are somewhere in between and it's up to you whether you call it a cake or a brownie.