Essentially Spiritual Warfare and Spiritual Combat are the same. Both phrases describe the fight we must take up as Christians so that we will enter eternal life and bring as many people with us as possible. I use the phrases to describe two different aspects of this fight.
I use the phrase "spiritual combat" to describe the spiritual battle we wage against our inordinate desires, our sin and our selfishness. It is the essence of the interior life. We combat the flesh and the passions in order to be able to embrace Christ more fully. Spiritual Combat is a quest for peace of soul. The best example to express my point is the book entitled, "Spiritual Combat." by Dom Lorenzo Scupoli. The book is all about entering into combat against anything that will keep you from fully embarcing Christ. It is a very deliberate method and plan of conquering sin and self. Spiritual Combat, while at times very physical, takes place in your own heart. It has to do with your own soul.
I use the phrase "spiritual warfare" to describe the battle we conduct against the evil spirits who constantly wage war against humanity. This is more of an outward battle. Under the heading of spiritual warfare would be topics like deliverance prayer, demonology, exorcism, intercessory prayer, the occult/ new age movements, protecting oneself from diabolical temptation etc.
How they relate:
As I stated before spiritual warfare and spiritual combat are essentially the same thing. I use them to describe two aspects of the one war we are in. Unfortunately too many of us focus on spiritual warfare when our focus should be on spiritual combat. Spiritual combat is the foundation for true spiritual warfare and our warfare will never be succesful if we aren't skilled in conducting combat in our own hearts and souls.