All the same conventions and lessons from typical music theory still apply in electronic genres, but I believe what you hinting at is some added emphasis on sound design. We sometimes take timbre for granted with non-electronic music styles, since there tend to be "tried-and-true" instrument/tone color combinations for most genres.
In synthesis, you have a lot of control over the timbre of each part at your fingertips. So much so that you might even be building up each sound starting from a sine wave as is the case for FM synthesis.
Many early synthesis focused on replicating timbres of real instruments, but some synthesis-specific descriptors of timbre have arisen over time:
Arp is a name commonly given to a staccato sound (or patch) suited for arpeggios. This developed in part because some prominent synthesizers (the Juno 60 comes to mind) included an automated arpeggiator to facilitate this type of playing. In the theme to Stranger Things you hear a typical arp sound throughout the piece.
Pads are sounds designed particularly for chordal work, and typically have a more ambient quality with slow attacks and long releases. It's kinda the synth equivalent to a string section. You can hear this sort of sound throughout in the background of the above piece.
Bass and Leads are pretty self-explanatory.
Then you can have some more genre-specific conventions for sounds, sometimes arising from a particular piece of gear that became popular during the time. An Acid Bass patch refers to the type of sound you can get from a Roland TB-303 while modulating the frequency and resonance controls.
In fact, most electronic styles have been influenced quite heavily by the gear itself. Most synthesizers through history have been best at repetitive patterns with different parts coming and going in piecemeal rather than sweeping, intricate compositional changes. Additionally, the "knob-tweaking" capabilities of most synths is an avenue for generating a lot of sonic interest in some styles. Acid house in particular is a good case study for how the style of a subgenre was heavily influenced by a particular instrument. Studying the equivalent development for other genres would be a good place to look for the "theory" of these individual genres.