After 2NT, 4NT is a quantitative raise, asking partner to bid 6NT with a 'good' 2NT. It is not Blackwood.

On Board 32, East's 21 hcp and solid 5 card ♦ make this a good hand, and the invitation should be accepted.

On Board 33, South's 20 hcp and missing K♠ do not constitute a good 2NT, and the invitation should be declined.

However, many pairs play Baron after 2NT. A response of 3♣ asks opener to bid 4 card suits upwards. This is similar to Stayman after 1NT, except opener will show 4♦, not just the majors. This is because a ♦ slam may be possible.

Many players would not use Baron with West's hand on Board 32, with its 3343 shape. It looks like NT is the right strain, since it scores more than the minor. But notice that 6NT depends on a finesse while 6♦ is absolutely cold (How?)

On Board 33, North has a 4234 shape. If opener has 4 spades, 6♠ might be better than 6NT. So here Baron makes sense.