"We all practice stalls at lower altitudes in training where all it takes is the addition of power and a slight lowering of the nose to recover."
More likely this is, stall warning practice or 'approach to stall'.
1. Stall warning = Approaching stall - Actions are required to avoid stall.
2. Stalled = Stalled - Actions are required to recover from stall.
3. Deep Stall = Stalled and no Pitch Authority - Recovery unlikely, at least by using elevator.
Some have suggested, or implied, that 'Deep Stall' may be defined as 'very much stalled', but this offers very little additional information than 'Stalled'. Which is why we refer to a Stall which has also removed normal pitch authority as a Deep Stall.