If we want to understand the difference betweeen a regular relaxation masage and a tantric one, we should look into the tantric teachings a bit.
Tantra is an eastern millenary esoteric system, which aims to gradually awaken the human being on different levels. The idea of tantra is to bring the sacred sexuality into our daily lives, leading to achieving higher spiritual states and expanding our consciousness. Tantra transforms sexuality in a way which makes it energetical support for our spiritual evolution.
The Western version of these teachings emphasizes love and touch. This is exactly what we can experience in a tantric massage, which teaches us selfless and spiritual attitude to other human beings. When a man makes a massage to his partner, he is not aimimg to satisfy himself and his senses, on contrary, he offers intensely something from himself and carefully expresses love without any expectations or conditions. We learn this way to give to another person something what s/he needs instead of giving what we think s/he needs.