By definition, grand strategy lets you take a race/empire/faction/nation through a series of wars. I admit, that's a very broad definition, and includes stuff like 4X games, total war series, paradox grand strategies (I'd say each is a genre of its own).
Main difference from Homeword and similar RTS games is the scope - you will be controlling the resources on a very high level, tackling political issues, economy, research, etc. and usually won't be bothering with ordering individual men around.
To illustrate it further, in a typical RTS game you are thrown around into battles and have to make do with what you are given, whereas on grand strategy level you get to affect who do you fight your wars with, where do you fight the battles and what
you are fighting with.
Regarding getting into a typical paradox-style grand strategy game like Hearts of Iron, Europa Universalis, Crusader Kings, I can't really help you here because I never could get any enjoyment from that.
Biggest obstacle is learning how to play the game and how to have fun with it, the in-game tutorials are pretty poor in this regard, so you're better served by let's plays and youtube.
Big part of the fun is playing out a scenario that is laughably improbable when it comes to real history.
When it comes to a more typical 4X game, you can approach these like a boardgame with AI opponents. The bit about laughably improbable scenarios still stand, but the point of games like the Civilization series is to throw history out of the window.
I recommend that you start with the classics here as the genre pretty much already gave us what it got best: Master of Orion 1 and 2, Civilization (4 seems like a decent starting point, and has plenty of excellent mods), Sid Meier's Alpha Centauri.
Most of these are old, so it pays to drop the graphics whore act asap.
Regarding Total War series, my opinion is that Total War War Hammer is pretty shite. Though if you want more where it came from, I'd recommend the first few games in the series. If you can't make it past the graphics, Shogun 2 is a decent compromise.
Rome 1 is also good and Medieval 2 is worth it with modding.