Both terms "control group" and "comparison group" are often used interchangeably to refer to the same thing—a group serving as a baseline for comparison with the group(s) exposed to an experimental treatment. However, some might emphasize the nuanced difference that results from the assignment of participants. In other words, a control group is randomly assigned while a comparison group is not. The following could be relevant.

Dettori, J. R., Norvell, D. C., & Chapman, J. R. (2019). Grab control! Choosing the right comparison group in an observational study. Global Spine Journal, 9(4), 456–458. https://doi.org/10.1177/2192568219847206

Good luck,

These two concepts are used mostly in experimental studies to check the effect of one intervention on the experimental group. The control group and comparison group in an experiment are more often the same. The control group serves as a comparison group for the treatments. By serving as a basis for comparison, the control group reveals the treatment’s effect.

In most cases the comparison group would be subjected to less control, but instead be allowed to vary in ways that any group might vary. The key issue is the degree of control; the point of a control group is that it is controlled systematically so that the areas in which it is controlled can be compared with the experimental group, and the difference would be the size of the effect brought on by the independent variable. Of course the terms in this last sentence relate to quantitative research, and thus in qualitative research the term "comparison group" reflects the lower degree of control inherent to the qualitative approach.

Was going to add an answer..but am happy to recommend the three above.