When running do you train for time (speed) or distance?

And when I do run in a race, I like to follow this principle:
Start out slow, then back off...

To avoid being run over by a bus, or to get a fresh beer during a commercial break.

You can do both, but I think one must be the "main effort" for each training session. I'm a distance guy. Most of my runs, especially the main one each week is a push to increase distance. That said, at least once a week I have a speed day. I run a shorter distance and try to drive down my minutes per mile time. So while I'm training for distance I want to be faster in my next distance race.