"Two-tone test" and "IMD test" are somewhat different animals.
Yes, one tone or nine tones are "modulation" BUT... IMD rears its ugly head when using solid state circuits with complex modulating signals (mainly voice or data)
A Two Tone test in radio has
traditionally been used to inspect for percent-modulation (over-drive that causes flat-topping or clipping) and amplifier bias (non linear region operation). That's much simpler than IMD testing, and doesn't require nearly as expensive equipment as IMD testing, and can be done with a cheap oscilloscope and a trigger signal. Part of that "traditional use"' is the fact that in decades past, especially in Amateur radio, test equipment was either not available or extremely expensive.
An early text describes two tone modulation as mostly related to amplitude distortion. Two tones in, two out, compare them. The text does mention frequency, but in the 1940s, again, who had spectrum analysis?
(Radio Engineers Handbook, Terman 1943, pp 966, 967, "Amplitude distortion in amplifiers")
The difference between one and multiple tone testing is that multiple tones can mix together and thru the modulation process, produce other signals that aren't supposed to be there. This is also a factor in amplifier 'overhead' or how much information (bandwidth) an amplifier can process.
Amplifiers are also mixers, tubes are the best, transistors the worst.
From Electronic Design:
Intermodulation distortion is an important metric of linearity for a wide range of RF and microwave components. Fundamentally, it describes the ratio (in dB) between the power of fundamental tones and third-order distortion products.
https://www.electronicdesign.com/technologies/communications/article/21798494/understanding-intermodulation-distortion-measurementsDistortion products consume part of the amplifiers overhead- they waste power and cause interference. Since that's in the voltage (power) vs. frequency domain, spectrum analysis is required.
That's not possible with a $50 'scope.
Notice the article mentions "harmonics." Those are mixer-products very close to the carrier frequency and require a good spectrum analyzer with very good RBW (or mod analyzer) to accurately measure, unlike a second harmonic of a carrier (2f, 3f...) which is far enough removed from the carrier frequency that most anything can detect it.
IMD and such complex parameters are often used in the context of device design and Regulatory Agency (US-FCC) certification and requires high end equipment for reliable measurements.
Oddly enough, a good radio receiver makes a fine 'seat of the pants' test- just listen to the received signal while tuning up and down in frequency.
To hear severe cases of distortion, listen around 7170 KHz (40M amateur band) to the operators grossly over-driving transmitters with audio processing equipment and notice the extreme distortion produced, in some cases, roughly half the transmitted power wasted in spurious products (and highly against FCC regulations, BTW).
Attached: a 'scope display of a two tone test I recently did on an old Drake TR3 Amateur transmitter, using an AWG and scope. It "looks" clean and regular, but that's deceptive, as it only shows amplitude versus time, not frequency. There must be distortions there which are not shown in that trace.