They both are for the 4wd system.
You use part time on very slick surfaces. It is for "part time" use.
You use full time on partialy slick pavement. You can use it "full time".
Check your fuses
Check fuse for tail and parking lights Could be a bad dimming rheostat Could be a bad headlight switch
Check your fuse. Usually the manufacturer has the dash lights and the tail lights on the same circuit.
you have a bad headlight switch. easy to change out it's just a tiht fit under the dash
in the bumper xx
if you have a tow package, check the wiring connector for shorts, some times they corrodes and causes a short circuit
Check fuse for tail/parking/dash lights
number 9 fuse under dash
You need a scan tool.
check the fuse for dash lights
blown fuse blown fuse
Short