Although both words are often used interchangeably in physics, there are a number of differences between them.
Pressure is used when referring to the amount of force that is applied to a given area as regards the surface area of the object.
Stress refers to the induction of force from within a body, per unit area.
While pressure is applied on an object from its external environment, stress is generated from the inside of the object and acts opposite to the direction of the applied force.
When excessive pressure is applied, the object begins to fold in on itself. i.e. it becomes compressed.
When an object is placed under excessive stress, it causes the object to become deformed or strained.