Slow burn, area-of-effect grenades, for instance, such as the Warlocks’ Vortex Grenade, are made for clearing capture-points, locking down entry points, and blocking enemy players from accessing ammo crates. You’ll explore this to a decent degree in PvP, but the faster, more aggressive, more demanding combat of the Crucible is where the various differences and strengths will really become apparent. They all have very different effects and strategic purposes. In Destiny, grenades are a lot more than simple throwable damage.
Always be actively aware of your current effective kill-range, and make sure that you’re equipped with something with the ability to cover anyone who might come up in line-of-sight, however near or far. When you head back out into the open, switch back. As you move into a tighter corridor, go close-range. Get into the habit of switching between your primary and secondary weapons as you move around the map, whether there’s any enemy in sight – or even on the radar – at all. The Crucible’s skirmishes are so quick to start that being reactive rather than pro-active is not going to do you any favours. If you’re switching to the appropriate weapon for an encounter as you run into it, you’re acting too late.