Is clenching and unclenching my sphincter the exact same thing as doing a kegel exercise?

No, but can be part. Your sphincter can be contracted during kegel exercises, but kegel exercises also include contracting gluteal (buttock) muscles plus thrusting the pelvis forwards.
Kegel. That is part of the kegel exercises. However, you want to make sure you feel all of your pelvic muscles tightening and untightening.