For all intents and purposes AWD and Full-Time 4wd are the same thing. However, in practice AWD systems don't offer low ranges, locked part time or 2wd modes. Also, many full-time 4wd systems don't offer options for 2wd like the np242 does. Mostly though if its a truck, call it Full-Time, if its a car call it AWD and you'll be fine
Yes, many AWD and Full-Time 4wd systems use a form of limited slip in the centre differential to modify the torque balance. For example. A 100% open diff in the centre will give you the theoretical 50/50 torque split - but it WON'T transfer any torque to slipping wheels whatsoever (np203 for example) so its really more of 100/100 split or not a split at all, if that makes sense.
In contrast to a locked part-time case which really is 50/50. If you add an limited slip, most common is probably the viscious coupling (np242 for example), it gives you SOME resistance to slip front/rear. Depending on HOW aggressive the LSD unit is, and its placement in the drivetrain they calculate the rolling "torque split".
Now some AWD systems get far more advanced and can actually dynamicly change the front/rear torque split. Automatic subarus have been doing this for years, amongst many others. They have a clutch pack, which under normal driving doesn't have much pressure at all on it making it virtually FWD. When the system detects slip it tighens the clutch pack creating a tighter connection to the rear wheels, on the fly.