Yeah, how you arrange the notes of a chord in terms of register is called a voicing. There are lots of different voicings that work for lots of different instruments, as well as an element of personal taste and choice.
It's too lengthy to go into, but you might just want to google "piano voicings", "guitar voicings" etc.
You can't make triads with one note instruments like a Trumpet, Sax, Oboe etc. because they can only play one note at a time. In those situations is when you would take those type of instruments and use them together to form a chord, like for C Major: a Trombone would play a bottom note C - an alto sax could play the middle note E - And a trumpet could play the upper G ... understand?
while using a sequencer and samples and stuff..you can write three note chords for monophonic(1 voice) instruments..in reality it would not work though..these instruments are only possible to use as multi voice instruments or polyphonic instruments in the digital/computer world.
some instruments like string instruments can play double stops..two voices at a time..but usually the chord is split up between multiple instruments(eg:string secction)the same chord but the three notes played by three seperate violins or 1 note violin,1note viola,1note cello..sometimes the whole orchestra plays a chord together called a 'tutti' played over maybe 4 or 5 whole octaves.sometimes instruments are doubled over an octave or sometimes in unison playing the same note...but just be aware about this...youcan write the same chord under one instance of the instrument..but this is not the way to write music if you ever want someone to play your music..
you should read a bit about instrumentation, orchestration and chord voicing.. ..every instrumet has its own capabilities and limitations..which you should slowly learn about...
i think it dosen't matter if you want to produce but dont know the basics yet..the fact that you are asking means that you are on your way to learing the basics...
anyway..
good luck
and open up some midi files and see what other composers have done..you can learn alot this way..
"Yes I understand. So there's no such thing as a trumpet chord?"
there is ...but not on one trumpet...three trumpets..thats why there are sections..
there are thousands of possibilities to split up a chord..voicing and voice leading are a whole subject on their own..each composer uses different voice leading patterns that are recognizable after a little practice.
thank you for the comprehensive post. Another question. How is e.g. a trumpet usually played in a pop songs. Single notes, or chords played via many trumpets as you explained?