The terminologies are often ambiguous, depending on the context.
"Easy pace" describes a pace level, which can still include a whole range of paces from recovery pace to anything below marathon pace.
"Easy running" describes entire session. Long run at easy pace is not easy running because of the duration.
"Base mileage" is about amount of running over a multiday period (usually per week). Not necessarily easy or hard. In base building period, it's recommended that the pace is mostly easy (in the sense that there is no tempo or fast interval, but there is quite a lot of flexibility, and can even include strides). The point is that ramping up base mileage is not an easy effort because you are adding duration, which requires recovery while still adapting to new mileage.
After you can do the mileage day in day out without the need of recovery, this becomes your new base mileage. The whole thing becomes "easy", with no need for rest days, no soreness, no accumulated fatigue. In this way, you can isolate the cause of fatigue once you add workouts (interval, tempo or long runs) in the next phase.
The above assumes you follow the approach of strict periodization, which is not the only way. Some people include all range paces throughout the cycle, and even at a single run, and only change the dosage/proportion subtly based on feel and feedback on how the body responds.