In the old days, some developers were formulated to be for both paper and film. This was convenient for the photographers at the time, and worked out more or less. As plates and paper were either home-made or of varying quality and Emulsion for plates and paper were more similar a century ago than today, these were average developers for average emulsions.
Today, film and papers usually are developed in specifically formulated developers, which will give optimum results for each. There are still some Universal Developers for film and paper out there, but the formulas are usually for one and are tweaked to fit the other. Besides these formulas should be tested how they work with each type of film/paper, as they will give different results.
I have not worked with caffenol-c. I understand it has been formulated as a film developer, and some people on the net say it´s good for paper, too. From the look of your prints, it seems either the developer was too weak (too little developing agent or alkali), exhausted (oxidazitaion or chemical contamination) or you had way too much restrainer. But that depends on the exact formula you used and the quality of the chemicals and possible interaction with the paper.
As you are just getting started, it is probably a good idea to get some pre-mixed print developer, e.g. Moersch Eco 4812. If you want to dive deeply into the topic, you can look for The Darkroom Cookbook by Steve Anchell (google has a preview of some pages).
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