Trying to patch areas of drywall texture
That looks somewhat like a "knock down" texture. The ceilings in my house look like this:



This type of texture can take on many variations of look which can depend on the consistency of the mud when it was spattered on, type of spray gun and nozzle used and how long the material has dried before you knock it down with a knock down tool or other wide drywall knife.

I had only moderate success trying to re-texture a bathroom where I had to open the ceiling to install some electrical wiring years back. I tried some of those spatter spray cans of texture that you can buy at the big box stores. My results after several practice sessions on scrap drywall were less than spectacular.

More recently I was trying to deal with matching a ceiling in a laundry room where about a third of the ceiling needed to be replaced with new drywall. Based upon my previous experience in that bathroom and the discussion on this question I decided to just skim coat the whole thing and leave texturing to the paint roller when installing the paint.