I would say that the hydro is intended to test and verify the metallurgical integrity of the material and construction of the bottle: expansion within tolerances and contraction when pressure is released (basically testing the elasticity of the bottle materials).
The VIP is more (mostly) an examination of the mechanical condition of the bottle which can be visually verified: absence of damage, absence of conditions that can impair the integrity of the bottle internally: water, oil, slime. But primarily pitting or rust/oxidation damage in the tank, along with examination of the threads under magnification to ensure they still comply with published specs (condition, number of continuous threads appropriate for rated service pressure, absence of cracks, crack vs tool marks in threads, condition of the inside shoulder of the bottle). The tech should sniff what's in it, look at what comes out of it, see if the interior is growing stuff or covered with oily slime. Check that it does not show evidence of excess heat (more of a concern on AL bottles as this thermal threshold is much lower for AL - one reason that repainted tanks are suspect and require further inquiry - powder coating a bottle is likely reason to condemn an aluminum tank), bottle shape or deformity (bow vs bulges), outside corrosion (why all stickers have to come off, or should, all accessories bands/boots must come off (NEVER seen this as part of the hydro visual)). All blistered paint must be scraped off. Scratches/abrasions/gouges - location, size, depth within published allowances. Valve condition is also assessed (thread condition, ease of us (turns freely), has OPR device, OPR device replaced or disk replaced at hydro interval. While these things may touch on safety to the person breathing out of the bottle, to me, these things are much, much more about fill station safety and the safety of the fill station operator.
P.S. - after I wrote all that, I found that Alec seems to be parroting my material.
Probably already seen, but pretty good demonstration/discussion of the VIP process.