Explain the practical difference? Player A is unhappy and wants to be traded but has full NTC and doesn't have to go to a team he doesn't want to. Player B is unhappy because the team wants to trade him but has has a full NTC and doesn't have to go to a team he doesn't want to.
This really isn't rocket science. I have no idea how this conversation has gone this long and you haven't been able to grasp that there is no practical difference here as far as the team having the leverage to force said player to go to a team that the player doesn't want to go.
The problem is you are assuming that all players who have NTCs and who are asked to waive their NTCs will be unhappy and not be willing to continue to play for their teams. This is obviously incorrect. We often here of players who are approach to waive their NTCs and who decline and thereafter continue to play for their team. We can also assume that this occurs and is never made public as well.
Your whole argument that there is no practical difference assumes that once you have asked any player to waive his NTC that such player will instantly become unhappy and effectively demand to be traded in the same way a player, like Kesler, who is unhappy and initiates a trade. This is very, very obviously not the case.
So there lies the practical difference. If a team requests a player to waive his NTC, and the player declines but is happy to continue to play for his team, then the team has no real leverage (other than perhaps threaten to waive the player). This is in stark contrast to a player like Kesler who has a NTC and initiates a trade because the team in this scenario can reject the trade request unless such player is willing to expand or waive his NTC. Obviously a team doesn't want to have a disgruntled player on their team, but the disgruntled player doesn't want to be there either, so the two parties both have leverage, compared to the other situation where only the player has leverage. And in Kesler's situate, he had TWO MORE YEARS left on his contract, and very obviously he didn't want to play out his contract in Vancouver, which is why Benning had leverage to get Kesler to expand or waive his NTC.