Drag radials and other R compound track tires are designed for two different purposes.
Drag radials are designed for the dragstrip. Design features to aid with acceleration runs include a very soft compound that doesn't need much warmup, and reinforced sidewalls so that they can withstand the deformation that occurs with low pressures used at the strip.
R compound track tires are designed for the racetrack. Design features include a relatively soft compound, but one which typically requires a couple of laps of warmup before they reach their performance potential. They are also designed to grip well while withstanding maximum lateral cornering forces as well as longitudinal forces like acceleration and braking.
That doesn't mean you can't use either tire for the other purpose, but its performance won't be optimal.
Also, when discussing Nitto's tires, don't let the terminology confuse you. They make the NT555 street tire, NT555R drag radial, NT555RII R comp track tire, and NT-01 R comp track tire.