What a watch measures
Heart rate, wrist motion, steps, calories estimated from all three. Useful for running and cycling, where effort and distance are the whole story. For a set of squats it can tell you that you worked. It cannot tell you how many you did or whether the last one finished.
What the camera measures
A skeleton, thirty times a second, with the position of hips, knees, shoulders and wrists. From that Strikt counts completed cycles, times them, and records pauses and pace. The phone sits still; nothing is worn.
Where Apple Health fits
If you connect it, Strikt reads last night's sleep and active energy into the morning check-in. If you do not, the check-in works on its own answers. Health is never required, and no data is written back to it without asking.
The honest limit
The camera needs to see you. In a crowded class or on a treadmill, a watch is the better tool. For bodyweight sets in a room where the phone can stand still, the camera is the more precise one.