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1.
Track Warrants and Timetable and Train Order control systems can co-exist.
Sometimes when TWs were being phased in (often over many years) trains operated using both (or more) systems.
I.E. A train might originate in a yard where movements are authorized by rule 105 (other than main track) rule and rule 94 Yard Limits (Main Tracks only). The YLs might extend a mile or two onto the T&TO controlled subdivision. The train might proceed to a branchline Jct. at which time it obtains a track warrant to Work for 30 miles on at TW branch. The branchline Jct might be a controlled interlocking once controlled by a local operator (or agent) who's job of copying TOs was replaced by TW, the interlocking now controlled remotely by a dispatcher.
Track Warrant forms are always evolving
Early track warrants as developed on various railroads were anything but uniform. To operate on another railroads version of TW one would have to be cognizant of the variations. I.E. on some railroads a patrolling foreman is issued an authority as a train and is thus met. On others the foreman is only issued a permit to occupy the track and the crew must contact the foreman and only proceed after written instructions are received.
The short point is that one should be aware what forms were in use during the era they are modeling as they changed often.
What's in a name?
There is a article in Trains magazine, possibly 1984 about the early history of Track Warrants and Direct Traffic Control the two dominant forms of control that superseded T&TO. Track Warrant Control Systems are related or have developed from other names such as Occupancy Control Systems , Manual Block Systems(Canada), ATCS, probably others.
One main difference between TWC systems and DTC systems are DTC systems rely on defined limits which are fixed and defined by signage located on the right of way. TWC systems in general have dynamic limits which are not fixed therefore no signage exists in the field to remind crews when the authority ends.
Some examples of Track Warrants are found at:
http://www.lundsten.dk/us_signaling/twc/