The distinction between honor and power is made in Ch. 11 when Jonas and the Giver are discussing individual choice. Jonas has just learned that this used to be possible and wishes it still were. The Giver agrees and Jonas replies, 

"But sir, since you have so much power..." (Ch.11)

and then the Giver quickly replies with,

"The man corrected him. 'Honor,' he said firmly, 'I have great honor. So will you. But you will find that that is not the same as power. (Ch.11)'"

What becomes clear is that while the community and the circle of elders all have great respect for the Giver and his position, he is not the one who makes decisions. He is the the one who advises the decision-makers. For example, he is much like a respected elder-statesman or politician who advises the President. That person might be well-respected (hence his/her advice is sought), but in the end the President still makes the decisions and has all of the power. That is the same in this book. He is only an advisor.