Certainly everything that has been said is technically true. It seems like efficient most often deals with timeliness and order - sense of organization. Effectiveness is "did it work?" So for a teacher, effective means, did the students get it? Often, some of the most effective teachers are the most inefficient, disorganized, always getting interrupted by the bell mid-sentence, scatterbrained, but awesome, teachers. The thing that makes them effective though, is usually charisma - which is a gift, not something you can necessarily develop through practice.
For the not-naturally-charismatic, I think there needs to be a balance. I personally consider efficiency to be effective. In this I mean that getting to the point (of anything, a lesson, a paper, directions) quickly and concisely is often the most effective.
Think about how many times you've tuned someone out because they seem to be talking and talking and talking and saying nothing. Neither efficient, nor effective. Case in point.