The biggest difference in indoor climbing is that your routes are mapped out for you. It can be challenging to figure out the proper sequence, but it's much easier if you know where all the holds are right away.
Another big factor is the abundance of large(ish) foothold. When setting in a gym (from 7 years of personal experience) even the tiniest jib can be very positive. Outdoors you struggle with purchase and deal with dirt/sand/etc... Which makes footwork even harder.
Some gyms make their grades soft on purpose, I've never really been able to understand why. They think it's beneficial to the beginner climber, but consistency is more important. Where I worked (in Seattle, WA) the grades would always stiffen back up when the setters got back outside in the summer, and soften a bit over the winter.
If nothing else, indoor routes are set with the intention of being climbed a certain way. When we set we know the moves will work. Outside it's just a blank canvas with a grade attached to it.