That first batch of studies all involved checks that forced the enemy king to move itself into a pin. But a check doesn't always force the enemy king to move; the other two possibilities are that your opponent might capture the threatening piece or interpose something between it and the king. Interpositions, like moves by the king, can lead to pins. Indeed, by assumption an interposition causes an enemy piece to pin itself. You then may be able to take it if you have enough offensive power at your disposal.
The importance of examining checks is especially great when the enemy king’s range of motion is severely constricted, as is the case for Black in the figure to the left. White has just one check to consider: Qe5. Black has no way to capture White’s queen and no way to move his king to safety. His only legal reply is to interpose his rook: Rg7, walking into a pin. Of course White will not be taking the rook with his queen; he will throw a cheap attacker at it with h5-h6. (Attack pinned pieces with pawns when you can.) The rook is lost.
The point is simple. Anytime a check you can inflict will cause your opponent to interpose something between his king and your attacking piece, ask whether you can throw any fresh attackers at the interposed piece; at least for the moment it will be pinned and unable to flee.