The phrase on the contrary is what you use to oppose a point.

For example , you decided to buy cheesecake at the cake shop . You mom is surprised because she thought you disliked it . Your reply would be " On the contrary , I've always liked cheesecake."

The word contrast is used to differentiate between two ideas. 

For example 

Red Velvet cake has a fluffy texture. In contrast cheese cake has a creamy texture.