Two sources for actual noise (not hum or microphonics) in tubes.
A long discussion:
https://static1.squarespace.com/static/5f0983034219c6086e8100ac/t/5f457a92bb0b1537ebdead39/1598388884791/Chapter+13+NOISE.pdf(1) There is inherent random noise from the flow (modulated by space charge) of discrete electrons.
The textbooks tell us that the equivalent noise resistance (a fictional resistor in series with the grid) decreases with transconductance:
RN = 2.5/
gm, approximately, for a triode, in the audio range.
(2) There is also "excess noise" due to strange effects on the cathode surface, which are not so predictable, but the spectral density goes as 1/
f.
It is also called "flicker noise" or "pink noise".
At higher frequencies, there is also induced grid current noise, due to impulsive effects from the electrons speeding past the grid wires.
The reports of higher noise for frame-grid tubes may relate to microphonics, due to the closer grid-cathode spacing (compared to conventional grid construction).
Otherwise, frame-grid tubes usually have higher transconductance than others.
Pentodes also suffer from "partition noise", due to the random fluctuation of the cathode current into its two sinks: plate and screen.
Connecting screen and plate gives almost the same behavior as a true triode.
There are possible defects in individual tubes, due to construction or deposition of unwanted material in annoying locations, over and above the inherent noise.