In a regenerative receiver, the amplified signal is fed back into the input where it is amplified again and again in a loop. Here is another description of it used in old radios:
It is basically positive feedback as in a Schmitt trigger. One would expect the output would go into saturation. What prevents it from going into saturation?
Mostly because there's a knob on the receiver that adjusts the feedback, and the user has carefully adjusted it to the point where the gain is just below the point of saturation (at least, for a classic regen listening to an AM signal). This provides a very high gain, but it does ultimately follow the input signal, and the oscillation will die away if the input goes away. If the knob is turned a little too far, the receiver does go into self-oscillation, then saturation, and the result is "howling".
Positive feedback, yes, "as in the Schmitt trigger", no.
The Schmitt trigger feeds back DC, is designed with a lot of positive feedback, and is designed such that the output voltage hits the limits cleanly.
A regenerative receiver feeds back AC at the desired receive frequency. This means that if the circuit does go unstable in the small-signal sense the result will be a more-or-less sinusoidal oscillation, not a "bang into the stop and stick" behavior of a Schmitt trigger.
A regenerative receiver is designed to have enough positive feedback to overcome most, or just barely all, of the circuit losses.
In the case of using one for AM reception, you do not want enough positive feedback to overcome the circuit losses entirely -- you want just enough to increase gain, with selectivity narrowed to the station you want to listen to. You do not want the thing to oscillate, and you don't even want the thing to become so selective that you can't understand what's being said.
In the case of using one for CW reception, you do want enough positive feedback to overcome the circuit losses, and a tiny bit more. You want the thing to be mildly oscillating. This way, what you'll hear will be the beat frequency between the incoming carrier and the internal oscillator.
In a regenerative receiver that's good for CW reception, this oscillation will be "soft", meaning that as its magnitude goes up, the effective gain of the regeneration goes down in a controlled manner. This, in turn, means that the amplitude of the oscillation will be somewhat controlled.
Because the performance of the receiver depends on this regeneration being just right, and because tubes were expensive enough that there were serious amateur radio operators using them, serious amateur radio regenerative receivers featured a regeneration control knob that varied some circuit parameter or another to control the regeneration level. Typically the operator would be adjusting this knob to the conditions and to the signals they wanted to listen to.
Usually there wasn't much attention paid to what happened when the oscillation voltage started "hitting the stops" -- this was an undesirable condition that the operator was expected to avoid by actively twiddling the knobs.
Modern regenerative receivers, where they're used at all, are designed with the expectation of low performance, and the regeneration "control" is fixed to a value that insures that each unit's (crappy) performance is good enough for the task for which it was designed.
The positive feedback in a Schmitt trigger is "self-reinforcing" ie, the output voltage rises uncontrollably like a snowball in an avalanche. Here, this effect is useful since it accelerates the transition and, in this way, it converts an analog circuit into digital one.
In amplifier circuits like Armstrong's regenerative circuit, the positive feedback is "dosed" so that there is no continuous increase in the output voltage, only some additional amplification. It is hard to imagine how this amplification happens, especially when we make a follower amplify (I suppose there is some effect of accumulation), but it is a fact.
It is interesting to compare the two types feedback circuits:
In positive feedback circuits, from a low-gain amplifier we get a high-gain amplifier.
In negative feedback circuits, from a high-gain amplifier we get a low-gain amplifier.
Historically, in the past they used positive feedback to make amplifiers because they did not have high gain amplifiers. Now we have amplifiers with excessive gain and we low it to get stable amplifiers with fixed gain.
In today's positive feedback circuits like Wien oscillator, the Armstrong's knob is implemented by a non-linear element.
