On a CDI ignition the ignition charged a very large capacitor. When the CDI box determines when the plugs should fire it discharges the capacitor through the coil. The capaxitor gets charged to a voltage much higher than the battery can supply. This as well as coil design creates a much stronger spark.
On the TCI it uses a transister to turn the coil on/off just like points do. With no moving parts it won't change timing like points. There's more to it on advance and such but these are the basics.
And as said by deadchef the XS650 never used a CDI.
70-79 used points, in 80 they started using the TCI. Stateside anyway, some places they used points past 80.
To rewire your bike, up in the XS650 TECH section you will find a link to Some wiring diagrams. Look through them, find one that uses the parts you have.
I like this one. It shows the basic points set up. It has boxes that have upgrades, like TCI, combo reg/rec and starter. Just swap the boxes to match what you have.
If someone swapped an older engine into your bike, they just left the points in the engine. Does it also have the advancer under the right side cover and the rod between them?
The points run off the cam. The TCI runs off the crank. The TCI box uses signals from the pick up on the stator. The pick ups get triggered by a magnet mounted in the rotor.
