When are cards not cards?

So i played
Commander Ulthok https://hearthstone.blizzard.com/en-us/cards/75639/

  • BC:Your opponent’s cards cost health instead of mana next turn .

Opponent plays
Grand Magister Rommath https://hearthstone.blizzard.com/en-us/cards/84003-grand-magister-rommath/

  • BC:Recast Each Spell you’ve cast this game that didnt start in your deck.

So as title of thread asks, how are the spells being recast suddenly not cards still? just because they are being recast, how does that stop them from being a card still? I understand the splitting of hairs when it comes to the difference of Play and Summon when discussing minions, and so on with Copies. What am I missing about the game mechanics that logically make something that is recast not a card?

Tangent: Why does
Perpetual Flame https://hearthstone.blizzard.com/en-us/cards/63098/ have a Recast that forces you to spend the mana for each Recast and get each Overload yet the Grand Magister Rommath does not make you spend the mana for any?

It’s not that they aren’t cards, it’s that they’re being cast by an effect so their cost isn’t paid (whether health or mana). Also overload isn’t a cost, it’s an effect so it has no interaction with ulthok.

My question about Perpetual flame had nothing to do with Ulthok. It was why each time you recast perpetual flame, you spend another 2 mana in addition to initial 2 to cast it to begin with. Noting you also get the overload each time you do. However Rommath spends 0 mana to recast every spell under the sun.

Perpetual flame does not force you to spend another 2 mana each time you recast it. Costs only apply when manually playing a card, not for card effects making you play a card.

Is there somewhere you can link to that spells out the nuances on Recast? the site and the game are not great places to look it seems. This game is becoming more like WoW where there is more homework needed to understand how to play it lol.