I do have Solforge but I just completely do not get how that game works. I've watched videos and had people try to explain it to me, but apparently I'm a dummy because I do not understand "deck building within-game" as opposed to how decks are made in Hearthstone (and other similar choose-M-of-N games).
I feel like this may be my fault. I was trying to explain why you discard your hand at the end of a turn in Solforge (it's a mechanic from deckbuilding, or "deck-building-within-game", games). That doesn't make Solforge a deckbuilding game.
Solforge and Hearthstone are TCGs, with traditional elements of constructed TCGs, where you build a deck before the game and play it with the goal of racing your opponent (generally by reducing their life total to 0 before they reduce yours to 0). Ascension and Dominion are deckbuilding games, where all players start with a deck that they improve over the course of the game, with the goal of having more victory points at the end of a game than all opponents.
The difference in feel between Hearthstone and Solforge is the resource mechanics, since there's no mana-type resource in SF. Your resources are moves (2 each turn) and cards in your deck (leveled-up cards are more powerful). You spend moves to improve both your on-board position (creatures in play relative to your opponent's) and your deck (playing a card levels it up), helping you draw more powerful cards later on. Cards in Solforge are not a limited resource since you completely refill your hand every turn.
Hearthstone is more Magic-like, where you spend mana and cards to improve your on-board position only. Cards are limited, in that when you spend 2 cards but only draw one per turn, you eventually run out of "gas." Hearthstone differs from Magic in that you neither draw a land nor are required to draw lands, so each draw is a card that does something ("gas").
Your ideas about what's good in Hearthstone will probably translate to Solforge more than you may think