Regular massage will use a broader variety of strokes from classical or sweedish massage as well as some of deep tissue. It will most likely be with more oil, different speed in different techniques and more oriented for relaxation. Deep tissue massage will be slow and deep, focused on deep tension and deep layers of muscles and connective tissue or fascia.
Be careful with other massage centers. Many therapist haven’t been trained in deep tissue massage. They just do a stronger massage with poor use of their own force. A good deep tissue massage might be intense in some parts of the session but you will know and feel the intentional purpose with your own experience.