Live Axle is an archaic and mis-used term. Some people use it instead of
Beam Axle which comes in semi-floating and full-floating, or in your case you meant that your front half-shafts don't unlock.
A
live axle is an axle that supports weight (which is what an axle does) and also provides the driving force. Your Ranger has a live axle in the rear, but not in the front. The front axles on the Ranger (any Ranger) are the little stubs. They support the weight but do not provide the driving force. No front axle is a live axle because the weight is supported by a seperate mechanism than the one the provides the driving force.
This is your basic live axle. It has the sprocket clamped to the shaft and the shaft drives the wheels and supports the weight.
This would not be a live axle. The axle is just a spindle that supports the weight only. Just like on any 4x4 front axle--Dana60 through SLA with CV shafts--or any full floating rear axle.
In the old chain drive trucks there was an axle that supported the weight of the truck and then each rear wheel had a sprocket to drive it with a chain with the differential inside the transmission. The weight was held by the rear axle and the driving force provided through the sprockets. That was a beam axle, but not a live axle. Like this 1925 Mack AC:
This is not a live axle because as you can see, the shaft isn't carrying any weight.
This is a live axle that came loose and it's obvious the shaft is carrying weight.
But like I said, it's an archaic term. Probably ATVs and go carts are the only people that use it.