In Shrader's Electronic Communications (1959), 13th edition Radio Handbook (1951), Henry's Radio Engineering Handbook (1959), Gray and Graham's Radio Transmitters (1962) and even Mr. Heising's original report from Western Electric (Proc IRE,1921), it is taught that Heising modulation used a big choke, with a class A audio and a RF stage both drawing plate current from it. This has also been known as constant current modulation. Oddly, my 4th edition of Terman's Electronic and Radio Engineering (1954) didn't mention the choke, only straight plate modulation. The earlier Terman Radio Engineering (1932) discusses many of the tricks of the trade, but at that time class B P-P modulators were new, and MOPA layouts were not practiced to a great extent. Modulated oscillators were the norm with an RF linear amplifier (class B) afterwards. Be glad those are no longer on the air! Terman himself had written a paper with John Woodyard at Stanford for IRE, on a new improved form of grid modulation with higher efficiency. But back to the topic at hand.... The distinguishing feature of Heising modulation was that the audio tube was single-ended class A and that the Z ratio was 1:1, so that the modulator was impedance matched to the RF tube supply impedance directly, with no room for adjustment with turns on a transformer. It was impossible to reach 100% amplitude modulation this way. Sometimes a resistor was included in the DC feed to the RF tube, to lower itís operating voltage, and allow the audio voltage from the modulator to fully modulate (100%) it.
Around 1932 to 1935 came the practice of plate modulation through a transformer, with a push pull class B audio stage driving the other side. Loy Barton of RCA expounded on the benefits in QST (1931). Art Collins discussed the problems of driving class B triodes in QST (1935). Barton's first paper on the new modulator was published in 1928 for his 1 kW AM transmitter at Univ. of Arkansas, titled "A Plate Modulation Transformer for Broadcast Stations", Univ. of AR, Eng. Exp. Station Bulletin #8. I've never seen a copy of this one - Loy Barton was quite a skilled engineer it seemed. RCA hired him away.
Plate modulation using a transformer to couple the audio to the plate voltage of the RF stage is also called class B high level modulation. The first paper that I've located which shows full plate modulation with a modulation reactor was Hutcheson's paper, Application of Transformer Coupled Modulators, from Westinghouse, Proc IRE,1933. He carefully explained the reasons for wanting to keep the DC current off the secondary, including this: "If the load direct current were allowed to flow through the secondary of the modulation transformer, it would produce a steady flux in one direction. Now during one half of an audio cycle, the flux caused by the audio voltage would be in the same direction, as that caused by the direct current, and for the other half cycle the flux would oppose that caused by the direct current. This the inductance of the primary of the modulation transformer would be reduced for one tube and increased for the other....the slight variations might still be sufficient to produce large enough even harmonic components in the output wave to make the use of the equipment impracticable." Hence the incorporation of a high value reactor in parallel with the AC path through the secondary. This is not Heising Modulation, however. The reactor's purpose is to present high Z to the modulator audio voltage output at even the lowest audio frequency, while allowing all DC to pass through to the RF tube. A capacitor is then used to block the DC from the mod tranny secondary. A modulation transformer is still used to impress the audio voltage from the modulator stage to the RF final plate voltage.
In Whitaker's Radio Frequency Transmission Systems (1991), a full blown plate modulated system is shown, with the classic reactor. No mention of Heising there. The 7th edition of NAB handbook (1985) probably is the best reference to explain the nomenclature. It agrees with the explanations above. George Woodard, former engineer for Radio Free Europe, and now back at Continental Electronics in Texas, wrote the AM chapter that year. Something noteworthy that he said is that this arrangement (Class B plate mod with a reactor in parallel) was used in high power transmitters until about 1960 when advanced core materials and careful magnetic design allowed elimination of the coupling capacitor and DC feed inductor (reactor), first in 100 kW European transmitters and then in American designs in the later 1960's. He said that the more advanced rigs eliminated the extra L and C and reduced the modulator from a three pole high pass filter to a single pole filter, greatly reducing low frequency transient distortion.
So our beloved 'hybrid' approach using a modulation transformer plus a big reactor is class B plate modulation, with the DC blocked. Its still found in many of the late broadcast boxes being converted for amateur service. It shouldn't be confused with the classical Heising modulation, where no transformer was needed, and a large DC choke was shared by the plate current feeding a single ended modulator and the RF tube.