MTS: Match production and inventory with consumer demand forecasts eg. Ikea. More push than pull because the item is produced to be in stock for the retailer.
MTO: Starts only after a customer order is received eg. airplanes. More pull than push. Raw materials you conclude, the manufacture does not know how to produce it based off how you ordered there. Only start a production when there is an order for you.
ATO: Production is built based on customers specifications from a stock of existing subcomponents. eg. car, you can decide what system you want, seats etc. This influences the decision/make of the car in the later stage. There is a little bit of push and pull. The car is assembled based off your choice.