I'd guess the CSA had a less developed system ? Although Porter Alexander is always portrayed in red trim.
You'd be surprised, starting out with literally no infrastructure, the Confederacy actually had a very well developed depot system by the end of war after they dropped the "Commutation System" where ladies at home made everything.
The CSA made every effort to provide red-trimmed uniforms whenever they could, (depends on
where and at what time CS artillerymen were as to what they were supplied), but for the most part they wore the same plain jackets that the infantry and cavalry. There wasn't a central government facility that provided every Confederate uniform, but many depots that did so, with one depot's products either slightly or very different from another's.
For example if an artillery battery was stationed near Richmond in the mid 1861-late 1862 period they would probably get a red-trimmed Richmond Depot jacket, or stuff from home, but from early 1863-real late 1864 they would get the same jacket but without trim and the same goes for other branches. In 1865, they could
usually be expected to be wearing either a Richmond Depot blue-gray kersey wool jacket, a jean cloth four button sack coat probably from the same place, or any of the variations of blue-gray kersey wool "Peter Tait" jackets imported from Ireland.
Now if we were talking of an artillery unit stationed in Texas, in 1861- to early 1862 they would either have what they could get from home, or a pre-war Union jacket. Throughout the rest of 1862 and into early 1863 they'll probably still have what they can get from home, along with drab or white jean cloth uniforms with no trim from the Houston Depot. Getting into late 1863 till the end of the war they would either trim-less blue-gray kersey wool uniforms or the same with red trim from the Houston Depot. At least on large detachment of several batteries moving through Texas had red-trimmed uniforms for everyone, brand new as in no one was in rags,
after Lee surrendered a month before when they learned the War was over, and every other branch was more or less about as well off.
Also to further confuse things it wasn't uncommon for an artillery battery anywhere in the Confederacy to be issued infantry blue-trimmed uniforms from a depot and infantry to get artillery red-trimmed jackets from the same place at the same time! Through the whole war I might add.
Everything in Confederate uniforms comes down to context really. Also what I've typed isn't even the tip of iceberg on Confederate uniforms, if you want to know more the best one stop place to get a idea is adolphusconfederateuniforms.com