What each of the 2 wires are called is dependent on the alternator naming convention being used.
Essentially the 2 wires will be ->
S (Sense):
The Sense wire (it goes to the battery so the alternator can sense the voltage for the regulator to do its busines). This wire goes direct to the battery (via a fusible link etc). No other loads on the fusible link (fuse etc) since it needs to accurately sense the battery voltage at the Battery+ post.
F or L or ... (Field, Light, ...)
This wire goes to the Alternator Light on the dash. The other end of the Alternator Light goes via the Ignition switch to Battery+. It's purpose is to provide initial field excitation for the Alternator to 'boot up'. During that pre-'boot up' time, the Alternator Light will illuminate with the key at the 'On' position. Once the Field starts up (alternator spinning), +12V comes OUT of the Field post and since the other end of the Alternator Light is also at +12V, the bulb goes out, unless of course the alternator is faulty. The Alternator Light needs to be an incandescent bulb to ensure sufficient current can flow through it to provide the Field Excitation, don't use an LED.
Your external regulator will have lots of connections, but there will be a Sense and a Field, you just need to identify them in your EWD. From you wiring picture, it would appear that your old alternator W-L wire is the Sense. And B-Y on the regulator will be you IGN+ to connect to the Field of your new alternator. It doesn't appear from the wiring snippet you posted that there is a Alternator Light??
cheers,
george.