Involuntary Actions are the actions of our body that are not controlled by our will. For example, heartbeat rate, digestion, etc. These are generally controlled by our brain.
Whereas Reflex actions are spontaneous, automatic and mechanical response to a stimulus action on a specific receptor without the will. For example, removal of our hand in a hurry whenever we touch a hot object by mistake. These are mainly controlled by spinal cord (modula avlangata) to fasten the reaction. All reflex actions are involuntary in nature but all involutary actions are not reflexes. A reflex action may involve any muscle or a gland as we withdraw our hand on touching a hot object but all involuntary actions involve only smooth i.e., involuntary or cardiac muscles.
Nerves and autonomic nervous system can increase or decrease the rate of involuntary actions but reflex actions can be controlled by great will only and are not usually controllable.
Reflex actions are done to meet emergencies where as an involuntary action may or may not be for just meeting an emergency; but may be an important life process such as circulation of blood, swallowing of food, movement of food in food pipe, etc.