The four quadrants are defined as:
Forward direction, forward torque (drive)
Forward direction, reverse torque (braking)
Reverse direction, reverse torque (drive)
Reverse direction, forward torque (braking)
In a DC SCR system, one needed two bridges to accomplish the four quadrants, if regeneration were to be the braking method. Contactors or reversing field supplies could be used to "switch" the leads to make one bridge behave like the two, but that's just engineering.
One can easily see that with three phase AC motor drive systems, the non-braking forward and reverse directions are easily accomplished with switching changes in the inverter. There is really no difference between these two quadrants other than "rolling the motor leads" electronically.
It is in the braking quadrants that we have problems (either direction). We draw energy from the line and provide it to the motor to inject energy into the motor when in the "drive" mode. Where do we put the energy from the motor when in the "brake" mode? Without a front end to invert the power back onto the line, the only answer is "dissipate it as heat."
Where we dissipate it as heat is the question. Your examples all dissipate the energy as heat in the rotor, or allow the inherent losses in the system to achieve the deceleration as in the coast stop.
Controlled deceleration just has the drive keep the motor fluxed during deceleration, allowing the drive to monitor the motor without the need for an encoder. Without maintaining rotor flux, the drive would have no other way of determining the motor's direction or speed. With no rotor flux, the drive would see zero motor Volts and zero Hertz, i.e., a stopped motor, even if it were actually still rolling. The drive could then conceivably plug the motor with very low frequencies trying to "start" the already rolling motor. This can cause not just heat in the motor, but can actually damage the motor or shear its coupling while fluxing the rotor. Reverse torque can be applied while trying to "start" a rolling, defluxed motor, causing severe torsional stresses. I once saw a gas injection fan (900 Hp, 4160V) shear its coupling in such a condition.
What we actually see as voltage on the motor is the back/counter EMF (CEMF) from the motor's regeneration. A motor has essentially zero resistance in its windings. Without CEMF, a motor would pull tens of thousands of amps at 460V excitation. The motor's windings actually see the difference between the applied voltage and the regenerated voltage (CEMF), and this is what mitigates the current draw.
Therefore, a motor must have rotor flux and stator flux to generate torque, and this rotating rotor flux generates a voltage in the stator that is opposite to the applied stator voltage. If you apply a torque opposite to the motor's direction, then the motor will stop more quickly (brake), but the energy that has been removed must be present in some form still.
So, to answer your question, you got nothing wrong and left nothing out, that I can see.
The old SCR switching AC drives had no way to convert the motor energy (without additional hardware). They typically used controlled deceleration to keep an "eye" on the motor during deceleration. The controlled deceleration essentially just provided magnetizing current, but no torque producing current.
If an LC filter were hung off the old-style drive, between the inverter and the motor, then the capacitors in the filter were prone to pump up during deceleration, and had to be monitored and protected. Without an output filter and without controlled deceleration, then the motor would just de-flux, and coast stop. This was because the motor had no path for its regenerated EMF and therefore no current would flow. Because no current was flowing, the magnetic fields would collapse.
Injection braking causes rotor heat. The amount of inertia will determine how much heat the rotor absorbs, and eventually dissipates, during deceleration. One can easily see that injection braking at a rate faster or more often than the heat can be dissipated will eventually overheat the motor.
I feel like I've taken over this thread. I'll stop now. Sorry for the long posts. I'm trying to illustrate a concept using words, without pictures or other illustrations, and that always takes more verbage than normal. I fear I'm causing more confusion than illumination, so will desist.
Regards,
Don