Ultimately, all three positions require a good core strength.

The wall chair works on your hamstrings, quadriceps, calves, and glutes.
The v-up hold works on your legs, abs, obliques, hip flexors, and lower back.
The plank works on your abs, back, shoulders, and neck.
Note: There's likely more that these positions work on and most of what I listed is surface-only research off of Google, so take what I say with a grain of salt.