CDI - Capacitor Discharge Ignition, a capacitor is charged up and then dumped through the ignition coil - fast, sharp hot spark, resists fouling, less affected by battery levels, often requires more components / complexity. Positive pulse from CDI to low-resistance primary ignition coil to ground.
TCI - Transistor Controlled Ignition, basically an electronic version of Kettering Points system used since 1913-ish. +12vdc ALWAYS applied to high-resistance primary ignition coil. TCI box grounds power for a few milliseconds each cycle, allowing current to flow; this generates a magnetic field in the coil core. When the TCI shuts the current off at the appropriate moment, the mag field collapses, inducing a big voltage in the secondary side of the coil. Very simple, but much more finicky in power requirements. Weak battery can cause hard starts; voltage drop in system due to cranking can leave the ignition system with nothing to use to make sparks.