running for time or distance
You can run for time, as in "How fast can I run 3 miles?"
You can run for distance, as in "How far can I run in 30 minutes?"
Or you can run for both, as in "I'm going running."
3 different strategies, with each needing its own mind set, goals, planning, and execution.
Running for Time
My fastest pace times come when I'm running for time. It's as if my mind & body are willing to sacrifice some pain, knowing the reward is I get to the finish line sooner; more pain = shorter pain. This is true whether I'm doing shorter runs (ie: 1 mile) or middle distance runs (3-4 miles). The mind set is that I'm going to push hard, I know my lungs are going to burn, and I'll watch the clock/gps to check my pace - knowing I'm going to push even harder if I fall behind. I use this method when I'm working towards a goal of trying to set a personal record for X miles.
Running for Distance
I struggle to push myself as hard when I run for distance. Unlike running for time, pushing myself early in the run only makes me more tired by the end of the run. Consequently, I end up pacing myself a little slower, and then kicking like heck at the end, when I know I don't have to save anything for later in the run. This means I don't always leave everything I have on the road, which also means my pace times aren't quite as fast. I use this method when I'm training for a shorter triathlon - knowing I will have already swum and biked, and figuring the run will take me approximately X minutes, I need to know I can run for X minutes regardless of how tired my legs are or how fast I go.
Running for both is another completely different mindset. I like to clear my calendar, give myself to permission to not think about the daily stress of emails, projects, etc., and just go running with a clear mind. I'll run for 60-90 minutes (no, I'm definitely not a marathoner!) without a care in the world. I get completely in tune with my body - my lungs breathing, my heart beating, my stride, my feet touching the ground. I feel the sun on my skin, and I hear the sounds of the surroundings - whether I'm in the neighborhood or out in the desert. I let my body go as fast as it wants to, which will change depending on the terrain. My average pace will be a bit slower, but my enjoyment of the run is significantly higher. I used this method to run two 10K's per week (one of them after biking for 90 minutes) earlier this spring while training for an olympic length triathlon.
Each method is very different. But all three methods are valid. I've said before, and I'll say again - you're only in shape for whatever it is you're in shape for. You can't be a great marathoner and a great sprinter (and a cross-fit expert, kick-boxer, swimmer, and rock-climber!) They all require different mental and physical training. And it doesn't matter which one you choose to work on. Just get out there and do it.