Don't read too much into slang. There are really only two types of ACM fights, Energy and Angles. The other terms you're using are slang for different tactics or maybe specific conditions of these two fights.
In a training scenario (specifically 1v1) which you use (Energy or Angles) is dependant on the strengths of your aircraft versus your opponent (max instantaneous and sustained turnrates, turn radius, energy addition rates, bleed rates, slow speed stabilityand maneuverability, departure resistance, etc) and the tactical situation (e advantage, defensive or offensive start, etc). An F4 vs an F14 would have to e fight if he wanted any chance to win since "slow" in a Phantom was anything less than about 450 KIAS and his turn radius was the size of Arizona (the state, not the ship) while a Tomcat would be capable of fighting below 200 kts.
There are two reasons to train for angles fights. It teaches you to maneuver at the edge of stall (the left side of the envelope) which is very different from corner velocity and above (the right side of the envelope). Being skilled in flying anywhere in the envelope is essential and, despite some common misconceptions an e fight can include maneuvering at the edge of stall. For instance, in an e fight you might do an unloaded vertical extension for vertical separation and then reverse over the top right on the edge of stall with your flaps and slats hanging out. It's not a "stall fight" (a term I never heard until AH), just a technique to reverse after getting the maximum possible separation. The second reason (and most tactically relevant) is that e fights tend to degrade to angles fights and an angles fight can get real slow (a "knife fight") real fast.
In a real world scenario with multiple bandits, inperfect SA, SAMs and AAA an "angles" fight (or getting slow at all such as the vertical reversal) is near suicide and is to be avoided. In an e fight, you maintain your e and options. With e it's possible to disengage when things aren't going right and bug out for home or get separation and then re-enter the fight ("redefine" the fight). It also gives you the essential maneuverability required to defeat a guns or AAM shot.
E fights, without discipline, almost always degrade into angles fights over time when a pilot thinks that if he gives up just a little more e he'll gain a few more angles or if he really becomes overly aggressive and decides to "sell it all" (sell all his e using his max instantaneous turn rate) to get a kill shot. If he misses he's slow and doesn't have much of an option to disengage especially if he's low (low, slow and out of ideas). Now it's a "knife fight". An in-close, slow speed angles fight to the death where neither aircraft has much of a chance of bugging out because there just isn't enough separation, and airplanes are slower than bullets so you live and die by the angles. Typically we're talking scissors maneuvers and lots and lots of rudder and afterburner and very few options.
"B&Z" uses elements of an energy fight but is just a tactic, it's not BFM and it only works when you have the e advantage. The correct RL name for this tactic is a "slashing attack". What people in AH call a "stall fight" is just an slow speed angles fight. A flat scissors is the best example, two airplanes riding on the edge of stall trying to get the other guy to fly out in front. Given two similar aircraft, he who rides the edge better wins (unless a wingman shows up and ends it). "Turn & Burn" is common slang for any ACM engagement with lots of g ("Turn") and afterburner (the "Burn"). Don't know if the term was used in WWII but it could have been if you consider "burning your e" but then e wasn't defined as a distinct element or until after the Korean War so it's doubtful.
Mace
