Matching previously applied wall and ceiling textures can be a challenge and somewhat of an art. In some cases you will have to smooth and retexture a complete surface (wall or ceiling) to replace it with something more consistent that somewhat matches it surroundings. That is mostly common in acoustic ceiling or (popcorn) ceiling removal.
There are a few ways that interior textures can be applied and often times you will have to experiment with material mixture and technique to match previous
textures after drywall repairs.
Hand drywall matching to a previous tradesman's technique will usually start out with a little bit of trial and error testing. Sometimes it's good to have a small piece of drywall to practice on. Some textures are applied with a pan and knife or a hawk and trowel. Some drywall textures make use of special brushes or swirl patterns in the mud. Some texture's are rolled on which is called stipple texture.
Here are a few of the more popular hand applied textures that I have had to match
Hawk and trowel (interior/exterior
Here are some of the more common spray applied textures.
Splatter knock down
I have attached some recent before and after pictures addressing this topic... smooth wall being the most time consuming