To my understanding, a massage parlour is a place for relieving stress, pain, and abnormalities in the body. While a spa is where you seek comfort, relaxation, and being pampered. Although in MTC terms, its pretty much the same since you'll likely get a massage and recieve some es in the end.
Edit: Noticed that pretty much every verified business here are "Spas". So basically mps are just unverified spas, like Goodlife, Caricia, Avalaya, and Relaxante.