The definitions/synonyms are kind of the same so I was wondering if they're basically just the same word or if one of them means one thing more than the other?
編成 is the organization or formation of a team, a military unit such as a fleet, a train, an orchestra, etc. When you use 編成, each member is basically a complete and independent unit (e.g., a professional musician) which can work even in isolation. 編成 means putting them together and make a greater system. The members are relatively homogeneous, and the resulting system can usually serve most of its original function even if some of its members are removed.
構成 is similar, but it's used with a broader range of words. You can say the 構成 of a sentence, software, a cell or a story, as well as a team of people. Each element or component can be almost anything, but it can be a thing which does not make much sense in isolation, like a tire and a CPU.
In places where 編成 can be used, 構成 could usually also be used without largely changing the meaning. But sometimes the meaning would change. For example, テレビ番組の構成 means a construction/format of a single TV program, whereas テレビ番組の編成 would usually refer to constructing the lineup of multiple TV programs for a day or week.
There is also 組成【そせい】, which is used mainly in technical contexts when each component is amorphous material such as oil and metal.
Finally, the definition of some online dictionaries such as jisho.org is often very insufficient. If you're an advanced learner, you can find many examples using ALC or Weblio.
In the case of the formation of a train, as cars in a row can be altered or replaced, I think that 編成 would be better. In the case of things that are more complicated/difficult to assemble 構成 would be used. In terms of a structure, which cannot be easily reformed or broken apart, 構成 would be preferable.