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Types of chess puzzles.
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It's a good list of the more or less orthodox chess puzzle types. Only you forgot the main one: directmate. Directmate is when the caption reads something like "checkmate in 2 moves".
Besides the orthodox types, there is a massive domain - thousands of types - of fairy problems for instance "capture chess" (mandatory capturing) and Circe (captured pieces return to home squares). We also get combinations of the types like "Helpmate in 3 moves, Circe and Capture chess". Chess composers invent new types by the day so the potential is infinite.
Games like "draughts" and "go" are simply outposts of fairy chess 
These are the types of chess puzzles. try posting some. enjoy.
A reflexmate is a chess problem in which white, moving first, must force black to deliver checkmate within a specified number of moves against his will - with the added condition that if either player can give checkmate, they must. If this condition applies only to Black, it is a semi-reflexmate. (Without this condition, the problem is just ordinary selfmate.)
A selfmate is a chess problem in which white, moving first, must force black to deliver checkmate within a specified number of moves against his will. Selfmates were once known as sui-mates.
A seriesmover is a chess problem in which one side makes a series of legal moves without reply at the end of which the other side makes a single move, giving checkmate or yielding stalemate, depending on the problem. Checks cannot be given except on the last move of the series. There are various types of seriesmover:
Seriesmate: a directmate with white playing a series of moves without reply to checkmate black (the seriesmover analogue to the directmate).
Serieshelpmate: a helpmate in which black plays a series of moves without reply after which white plays one move to checkmate black (the seriesmover analogue to the helpmate).
Seriesselfmate: a selfmate in which white plays a series of moves leading to a position in which black is forced to give mate (the seriesmover analogue to the selfmate).
Seriesreflexmate: a reflexmate in which white plays a series of moves leading to a position in which black can, and therefore must, give mate. Further, white is obliged to mate whenever he can, therefore he has to avoid in his series of moves aposition in which he would have mating possibility (the seriesmover analogue to the reflexmate).
A helpmate is a type of chess problem in which both sides cooperate in order to achieve the goal of checkmating Black. In a helpmate in n moves, Black moves first, then White, each side moving n times, to culminate in White's nth move checkmating Black. (In a helpmate in two for example, sometimes abbreviated h#2, the solution consists of a Black move, a White move, a second Black move, then a second White move, giving checkmate.) Although the two sides cooperate, all moves must be legal according to the rules of chess.
An endgame study, or just study, is a composed chess endgame position—that is, one that has been made up rather than one from an actual game—presented as a sort of puzzle, in which the aim of the solver is to find a way for one side (usually White) to win or draw, against any moves the other side plays.
In chess, retrograde analysis is a computational method used to solve game positions for optimal play by working backward from known outcomes (e.g. checkmate), such as the construction of endgame tablebases. In game theory at large, this method is called backward induction. For most games, retrograde analysis is only feasible in late game situations of reduced complexity, such as a chess position where few pieces remain in play.
A proof game is a type of retrograde analysis chess problem. The solver must construct a game starting from the initial chess position, which ends with a given position (thus proving that that position is reachable) after a specified number of moves. A proof game is called a shortest proof game if no shorter solution exists. In this case the task is simply to construct the shortest possible game ending with the given position.