Throughout the whole digestion process, food will pass from your mouth to your stomach before finally being processed into waste and expelled from the rectum.
You are right that there are two types of digestion that there are two types of digestion, mechanical and chemical.
Mechanical include such action as the breaking down of food by chewing with your teeth that forms the food into a pulp and also throughout your whole digestive tract peristalsis helps through the contraction of your intestine, throat and stomach to help food pass through.
Chemical digestion involves breaking down of food through chemical means like the amylase enzyme from saliva that coverts starch into maltose.
Stomach acids, bile, lipase and various other chemicals secreted by the various organs also include chemical digestion.