Conventions in depth
In a game-forcing auction with a major agreed, 3NT shows real slam interest and a cue-bid shows only mild interest.
Once a major is agreed in a game-forcing auction, either partner may start control-bidding toward slam. Some cue-bids show real interest and some only cooperate: you cue-bid because partner might have extras, not because you do. Without a way to tell the two apart, the partnership can end up in a doubtful slam that neither hand really wanted.
With a major agreed in a game-forcing auction, the hand to move chooses by strength:
Serious 3NT applies in a 2/1 game-force auction once a major has been agreed at the three level, the two natural shapes being:
It is not part of the Jacoby 2NT auction: there, opener has already shown shortness or extra strength, so that sequence goes straight to control-bidding without a serious-3NT step. Nor does it apply to a non-forcing jump raise (1♠ – 3♠), which isn’t a game force in the first place. It applies to both major fits, hearts and spades.
The difference is bidding room. With spades agreed, 3NT is the cheapest bid available above 3♠, so the two meanings stay apart: 3NT is the serious try, and control cue-bids begin at the four level.
With hearts agreed, a spade control can be shown by 3♠, which sits below 3NT. That does not block anything:
Serious 3NT works closely with Control-Showing Cue-Bids: 3NT sets the seriousness, the cue-bids fill in the controls, and Roman Keycard Blackwood counts the keycards once the picture is complete.