Pilates targets all the muscles associated with the core.
Pilates is a moderate, low-impact workout that targets major and minor muscle groups to strengthen your core like your deep abdominal, back, and pelvic floor muscles and balance your musculature. Pilates, unlike standard weight-bearing workouts, combines strengthening with concentric (shortening when loaded) and eccentric (lengthening while loaded) muscle activation to help you grow long, thin muscles.
Most people believe they are strengthening their core by doing sit-ups and other variations. In reality, they are simply using the outside layers of their abdomen and, in certain cases, their hip flexors (thus 'cheating' on the set).
The genuine core muscles are far deeper and include several muscles in the lower back. Pilates teaches you how to engage these muscles, as well as the outer layers of the abdominal muscles, to ensure that you're not lying or tricking your way through each repetition, allowing you to get the most out of each one. It is one of the reasons why Pilates is the perfect core training.