Are the games in the "strategy" genre always categorized under either the "turn-based" (TBS) or "real-time" (RTS) subgenres?
Are all strategy games categorized under either "turn-based" (TBS) or "real-time" (RTS)? Are there strategy games that are neither turn-based nor real-time?
No, Strategy games have an array of subgenres they can specialize into. Most of them are some kind of form of Turn Based Or Real Time Strategy, but there are exceptions.
The main contenders are Tactics style games which usually take place at a lower level than a strategy game - often focusing on individual units rather than grand force movements. Tactics can straddle both Real Time and Turn Base Games, and don’t really fit into either category.
A clear example of this would be the X-COM franchise which has both Turn Based Tactics and base development strategic resource management, depending on your current activity. Because of the duel-gamemode aspect of X-COM, while it leans towards a turn based style, it doesn’t really fit into Turn Based or Real Time Comfortably.
In a similar vein, Tower Defense games are generally considered strategy games but don’t really fit into the dynamic battlefield aspect of real time strategy games, and certainly don’t fit into the turn based aspect of strategy games.
There are a lot of different subgenres and it’d take too long to review all of them. Instead, I recommend looking at the https://en.m.wikipedia.org/wiki/Strategy_video_game and seeing if any of the subgeneres interest you