You should tip the massage therapist. A physical therapist makes around $65K/yr while a massage therapist makes about $35K/yr, which is why you don't need to tip the PT. However, PT's generally enjoy gifts and edible treats :)

There isn't a clear cut answer. Some people feel there is a difference in where the massage is being done. If it is being done in a spa/resort/hotel type place then it is customary to tip. Then if they go to a private establishment, they may not tip if they know that the person doing the therapy will be getting the full amount of the fee. But many people tip there also as a way to show their appreciation. Some tip according to the reason they are going to an MT. If it is more of a relaxation-stress relief experience you might want to consider the same tipping rules that apply to other personal services such as hair styling or spa services. If the massage is more clinical in nature, tipping may not be expected or even desired. Some therapists who work with referrals from doctors, dentists, physical therapists, occupational therapists etc. consider themselves on par with those professions and as such have a “no tipping” policy. Clinical settings usually welcome tips but don't expect them. Regarding the amount to tip, there are no hard fast rules to follow but generally consider $5 an acceptable minimum. The particular setting and price paid has perhaps more to do with the amount. A $2 tip could be viewed as insulting in a high end spa (like giving a waiter $0.01). If you choose not to tip, it's a kindness to refer the therapist to friends and family instead of the tip.

For the spas I go to for a massage a tip is expected.