One thing you should keep in mind OP is that "Strategy" is an umbrella term that includes drastically different games at the ends of the spectrum. Real Time Strategy on the other hand is a much more specific definition. To give you a very quick overview to help you orientate if you look/read about Strategy games:
Real-Time Strategy
Examples: Warcraft, Starcraft, Command&Conquer, Age of Empires
The game is played entirely in real time. You collect resources from the map using some of your units, and spend them to build new buildings, develop improvements and create units. It usually ends up in a military fight, but resource efficiency and build order (in what order you build/develop what) are extremely important.
Turn-Based Stategy
Examples: Total War, Heroes of Might and Magic, Civilization, Endless Space
The common element in all of these games is that you tend to play longer matches where you develop and expand an empire in a more meaningful way. You still collect resources to some capacity, and you definitely build, develop and muster military forces, but this "level" of play is turn-based and it contains managerial elements (for example, you have upkeeps that can drain your resources even without spending them, there are random events with various effects, sometimes you have to account for public order and rebellions in cities etc.).
Battles are a completely separate matter from the rest of the game mechanics, and when they happen each game manages them very differently. Sometimes you have very little decisional power and it's mostly a number games solved automatically, other times you might play some kind of positional battle that is also turn-based, or you might even have complete control on the units on the battlefield and the game becomes a full-blown Tactical.
If Real Time Strategy games are for the most part standardized in their mechanics and game flow, Turn-Based Strategy games can vary immensely. Some are incredibly deep on the managerial layer (Europa Universalis) but less focused on the battles side of things, some are lighter on the management but a lot deeper and more engaging with battles (Total War). It's an entire spectrum that really varies on a game-by-game basis.
Everything where you have a good level of managerial control over your empire is often called a
Grand Strategy, while other games that focus more on other aspects, like survival, exploration or development of individual characters you control, can be considered hybrids with another genre from which they take concepts and mechanics (for example, I'd call Heroes of Might and Magic an RPG/TBS hybrid).
Tactical
Examples: Company of Heroes, Homeworld, Dawn of War 2
Another very wide term that basically only says that 80-to-100% of the focus is given on the military aspects of the game, rather than resource management, faction development or management. Usually in real time, but can also be turn-based (at which point, though, people usually start calling them a Turn-Based RPG or a hybrid, like XCOM); you might still create new units on the spot, you might just have use what you are given. Most add more depth to battles compared to RTS games, by giving more importance to positional combat, use of the environment and specific unit match-ups.
Basically, what you want to look into if you don't like slow build-ups and management.
Construction and Management
Examples: Caesar, Anno, Tropico
Most are also called
City-Building games. On a technical level they usually play out similar to an RTS, as in everything is confined to a small sandbox "battle-map" played in real-time where you can build and create more or less freely. However, these games have very little to no military aspects, pushing the management aspects up a lot instead. You often have a financial balance than can go in the negative, population needs to satisfy by providing facilities and access to goods, and random events to mess up things for you.
Of course, this is just an overview. There are a lot of games that defy definitions, either because they mix elements of different sub-genres or they do things completely different than most other games. Honourable mentions in this group are games like Stronghold (City-Building/Tactical hybrid), Praetorians (Tactical with light RTS elements) and Majesty (kinda City-Building? Very unique and hard to describe).
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