Trimming, shaping, and polishing toenails as well as performing foot massage is called

The term for trimming, shaping, and polishing toenails, along with performing a foot massage, is known as a pedicure. This practice specifically focuses on the care of the feet and toenails, offering both aesthetic and therapeutic benefits. A pedicure typically involves soaking the feet, exfoliating the skin, and addressing the health of the toenails, making it distinct in its goal of enhancing foot beauty and hygiene.

In contrast, a manicure pertains to the same services but is focused on the hands and fingernails. Massage alone, while beneficial, does not encompass the nail care aspect. Nail art refers specifically to the decorative aspect of nails, mainly applied as a finishing touch on manicured or pedicured nails, but does not include the base services of trimming or polishing. Thus, the comprehensive nature of the foot care services entailed in the definition of a pedicure makes it the correct choice for this question.