No ^^^
GVWR = gross vehicle weight rating, this is the vehicle's load rating total: vehicle + passengers + load in the bed
GCWR = gross combined vehicle weight rating, would be the number that would be GVWR + trailer's total weight
So GCWR would be what the truck and trailer weighed if you pulled it on to a truck scale
Here is a 2003 Ranger spec guide:
https://www.ford-trucks.com/specs/2003-2/2003-ford-ranger-specifications/
Scroll down to Base Curb Weight, under GVWR is that models base weight used to calculate max load in the vehicle, Total Weight is actual GVWR for that model, Rangers are all rated for 1260lbs load, 1/2 ton(1,000lbs) + passengers(260lbs)
Then down to Towing Weight, thats where you see GCWR
Automatic trans is much stronger than manual trans, so automatics have a higher tow capacity, no it has nothing to do with driver skills, lol, its just strength of the parts
So there are two towing capacities, with automatic and with manual
Also engine size and axle ratios, 2WD or 4x4
Basically you subtract Base weight from GCWR to get max trailer weight, assuming no load in the bed, as you add weight to the truck the trailer weight maximum must go down.
Trailer hitch also needs to be rated at at least 10% of trailers loaded weight, so if trailer and load weighs 4,500lbs then hitch needs to be rated for 450lbs
Lightest Ranger weights 3,000lbs, 4x4 extra cab 3,700lbs, so that plus the weight of the empty car trailer will the total weight.
Can your Ranger tow it?
Yes, shouldn't be a problem
May your Ranger tow it?
No probably not
"Can" is the ability to do something, most any Ranger can tow 5,000lbs, even 4cyl, although not very fast, lol.
"May" is the permission to do something, in this case is it Legal for you to tow that much weight on a public road behind your Ranger
The Ford towing guide for your Year Ranger will be the Legal limits used by police and insurance companies, so just a heads up