@Fugue
Most (if not all, not 100% sure) cards that are in the Core set are a different version that looks the same as a card in another set. For example Noble Sacrifice (currently) exists in Core (uncraftable, as all Core cards); but it also (permanently) exists in the Naxxramas set, where it is a craftable card. Though they look the same, they are in fact different and you can own both the Core copies and the Naxxramas copies, or only the Core copies.
When searching for cards in multiple card sets, the game will typically show the Core version for cards that exist in Core and in another set as well. To find the other version, you have to select a specific set with the set selector. So if you just search for Avenge you will see the Core version, and not be able to craft it. But if you set the set selector to Naxxramas and then search for Avenge, you will see an option to craft it.
The two examples you mention are special in that both Truesilver Champion and Consecration exist in the Core set and also in the Legacy set, which now hosts a lot of cards that used to be in the Basic set that was given for free to all players upon reaching certain levels. So these cards are uncraftable in both sets. The Core version should be given to all players, but can be removed from your collection when the Core set is changed (which happens once a year). The Legacy version should, according to the Hearthstone Wiki, be given to players upon graduating from the Apprentice ranks (aka the New Player Experience) into Bronze 10.
See https://hearthstone.fandom.com/wiki/Truesilver_Champion and https://hearthstone.fandom.com/wiki/Consecration.