There is more to a beneficial massage than how hard someone presses on your body, and deep can happen more ways than painfully.
You can get massage from yourself, from people you are comfortable with, and from massage professionals of many kinds. I always want a treatment that makes me feel better now and also tomorrow.
A sensation of tightness can be relieved many ways. Manually moving the muscles enhances circulation of blood and warms the connective tissue within and surrounding the muscles. Passive and active stretching (non-painful) also are helpful.
A sensation of soreness can be relieved by stroking, kneading and shaking, all of which can and should be done without causing more discomfort.
If a muscle is only sore but hurts when it is pressed on, you can try another technique to reduce the soreness without causing pain.
A sensation of pain in a muscles can have more than one cause. If some part or all of the muscle is spasming, this should be released as soon as possible. Direct pressure and stretching are two common techniques. If those do not relieve it, other techniques are: holding the muscle in a shortened position, bending the muscle, or releasing the opposing muscle. A spasm injures the muscle, and that area needs recover time. It will be sensitive and is vulnerable for re-injury. It is not helpful to repeatedly press on it, over stretch it, or place too much load on that muscle. It can be helpful to relax the muscle (pain is not relaxing) and relieve residual soreness through gentle movement, warming massage, hot bath, ice, etc.
A Trigger Point is a place within a muscle that is tight and hurts and also often refers pain to other places. It is good to relieve the place that has the small spasm. The referred pain will feel like you can’t put your finger on it, and pushing hard on that area will not bring relief.
If I muscle has a tear, even microscopic tears, this will be very sore, and further injury can be caused by pressing hard on it or stretching it forcefully.
If a person has nerve pain, any place where bone, overly tight muscle, or swelling is pressing on the nerve can be causing that pain, and finding ways to relieve that pressure and make space for the nerves can be helpful, but nerves do not like being further compressed.
Connective tissue benefits from being warmed so that it becomes more elastic and slowly moved and stretched where it has become constricted. But connective tissue can also be overstretched, inflamed, or injured, and in these cases deep massage would have a negative effect.
So, let relief be the guiding goal, and find what reduces the discomfort without causing more pain. Beyond yourself, your friends and family are massage professionals, people who do energy work such as reiki, people who use traditional Chinese medicine techniques such as acupressure and acupuncture, doing meditation, and more.