Does an OTA Update erase all settings?

I recently did an OTA Update from 0.12.0 to 0.13.b3. It said the update was successful but then the device dropped off of my network. I thought the update was corrupted so I took down the device, plugged it into the cable and reprogramed it to 0.12.0 and it worked again. I updated back and fourth a few times and when I loaded 0.12.0 it would work (no setting up WiFi or anything). When I loaded 0.13.b3 I 'd have to setup the WiFi info before I could see it.

Is 0.13.b3 looking to a different location in FLASH for settings than 0.12.0 does?

Depends on the partition type the firmware is built with.
I recommend partitioning ESP separately with 1.5+1.5+1 MB scheme and then uploading FW.
Newer firmware may come with this partition scheme which will require erasing flash.