I call the eclectic technique I use in my oil massage 'Therapeutic Massage'. I cater each massage towards the individual client and their needs. The pressure applied varies depending on the individual and the intention of the treatment, e.g. to relax, to energise, to detoxify, to balance, to mobilise. A deep pressure may be used on a healthy, strong body where there are muscular aches and pains. The deep pressure stimulates blood flow to congested areas, boosts the lymphatic system to rid the body of excessive toxins from certain areas and promotes joint mobility. It also helps the body rid itself of old scar tissue. 
In many instances, however, a gentle massage may be more appropriate. Some bodies respond more positively to a more subtle approach - this is particularly true for people who are more sensitive to touch, or for those who have injuries. The muscles, tendons and ligaments are encouraged to relax through therapeutic touch, which in turn relaxes the nervous system, which encourages the body to switch over to the healing mode. 
On some individuals a combination of different approaches may be appropriate. 

My initial training was in Sports Massage (1996, St Mary's University College, Twickenham, UK - ITEC Level 3 Diploma in Professional Sports Massage), but since then my technique has metamorphosed into a more holistic and subtle approach. Subsequent trainings has led to the inclusion of techniques learned from Thai Yoga Massage, Shiatsu, Aromatherapy Massage, and most recently, from Tibetan Universal Massage, which specialises in treating soft tissue strain, trauma, and chronic conditions such as arthritis, asthma and tension headaches. I still hold a high regard for Sports Massage, but prefer to leave this to those practitioners who work specifically in this area, and who are exposed to a wide range of sport injuries.