"Thinking more moves ahead" is generally known as
tactics. When you are just going through
lines of moves in your head to see which is best, you are using tactics. There are some general tactical
themes that can be identified quickly if you know what to look for. These include
pins,
forks,
double attacks,
x-rays,
skewers,
diversions, and
discoveries. This is generally where a
computer excels.
Thinking more broadly is known as long-term strategy. While tactics focuses on winning material, strategy focuses on other factors that give you an advantage: Space, time, etc. An example might be not trading off a bishop of yours when you have a bishop pair and your opponent doesn't. I have a suspicion that GMs are not only excellent at tactics but also have a broad knowledge of strategy.