I know SRBs have a quite bit of thrust oscillation, and it's pretty much part and parcel of burning solid propellant. Do liquid-propellant engines experience something similar albeit at a much smaller magnitude? If so what is the main cause of this constant small variation in thrust level? Is it because of the combustion process inside the bell? In Falcon 9 launches you often see photos like this The streak patterns of the exhaust plume indicate there is at least some non-uniformity of the pressure and temperature field inside. I assume every liquid engine actually behaves like this, but it's only apparent on LOX/RP-1 engine because of soot acting like temperature indicator through the intensity of the glow for the pattern.
Yes, in liquid engines this phenomenon is called "rough combustion".
Sutton (4th edition) says
Combustion that gives pressure fluctuations greater than about +/- 5% of the mean pressure at a chamber wall location and which occur at completely random intervals is called rough combustion.
It's different from "combustion instability" defined as activity which
displays organized oscillations ocurring at well-defined intervals with a pressure peak that may be maintained, may increase, or may die out.
pp. 257 - 259
The streak patterns you mention are more likely due to non-uniform mixing resulting in slight variations in local mixture ratio, than due to rough combustion, IMHO.
In addition to the "rough combustion" that Organic Marble mentions, liquid engines also characteristically suffer from pogo oscillation. This is the phenomenon in which the thrust causes acceleration of the rocket, which changes the flow of propellant in the lines fuel and oxidizer lines, which then causes a change in the thrust, which is now a loop.
Pogo oscillation was a major problem in the development of the Saturn rockets, and I believe the Jupiters before them.