Wasn't intended for you specifically, just a general post in the thread that happened to follow yours. Glad you're not confused, neither am I.
Explaining the physics to some one who is confused can be a challenge, as you can see from the length of this thread. I'll let everyone else argue over the terms and nomenclature, fact of the matter is, if you make a turn to fly with the wind (down wind) the plane needs more speed in relation to the ground than it does while flying against the wind (up wind) to maintain the same airspeed. Air speed is what keeps the plane flying and Air speed does not "magically" follow the plane automatically when you turn down wind. There is a loss of momentum involved, so you will either experience a loss of altitude while the air speed is re-gained, or you will have to increase throttle until air speed is re-gained. The mistake usually happens when you try to maintain altitude during this turn with out increasing throttle, this is when you will be most likely to stall, even if your ground speed remained constant.

Simple fact is, if you turn down wind and your air speed is barely above stalling, to keep from stalling, you must increase power, or you give up some altitude to gain speed, or both.