First I've ever heard of "part time" 4wd. That 4WD button is responsible for sliding the selector fork in the front diff over to engage it. As I remember it (before I did the 5spd swap) the front drive shaft was always engaged. All the wheels were waiting on was that front diff to be engaged to get power.
It may be the first time you've heard the term "part-time" 4wd, but nevertheless that is what it is.
Furthermore, the transfer case in a '96- '98 Limited is not sending power to the front end, until the 4wd button on the transfer case lever is pushed. Or on manual J-shift transfer cases until the lever is moved from 2Hi to 4Hi.
Doing so moves a shift fork in the transfer case, which engages a chain coupling in the transfer case, which in turn sends power through the inverted tooth Morse chain to the front output chain coupling, which is splined and bolted to the front output flange, to which the front driveshaft is bolted. Thus sending power through the front driveshaft to the front differential.
The front driveshaft IS NOT always spinning.
From the factory, we have what is called A.D.D for Automatic Disconnecting Differential. In such a system, the driver's side front CV-axle shaft is always spinning the side gears and spider gears in the front differential when the vehicle is moving. The passenger side CV-axle is spinning up to the A.D.D coupler. When the 4wd button is pushed on the transfer case lever, (or the lever manually shifted for manual systems) the transfer case sends power to the front output, (as I previously described) while the A.D.D coupler simultaneously engages the front right passenger side CV-axle to the front differential. As you described in your quoted post.
Part-time 4wd means there is no differentiation between the front and rear driveshafts. Since there is no differentiation between the front and rear driveshafts, the driveline can bind and even possibly break parts, if the part-time system is used in high traction situations. Hence the recommendation to use it when road conditions allow some wheel slip, to help alleviate binding and potential breakage.
Full-time 4wd traditionally has meant the vehicle has a high and low range transfer case with a differential in it, which allows the front and rear driveshafts to turn at different speeds.
All-wheel drive (AWD) traditionally has meant a vehicle with no low-range, which can send power to the front and rear driveshafts, and allows those driveshafts to turn at different speeds from each other. That ability means it can be used all the time, on any surface without the driveline binding.
That said, AWD is the term usually used on this board, for the Full-time 4wd capability which some years and models of 4Runners have.