You are right. Hazardous locations have "classes" too but you are referring to article 725 here. It is generally called "low voltage" but that is not really true. Class 1 can be line voltage, class 2 is low voltage and class 3 is just a bigger class 2.
This is the commentary from the handbook.
GENERAL DISCUSSION OF REMOTE-CONTROL, SIGNALING, AND POWER-LIMITED CIRCUITS The wiring methods required by Chapters 1 through 4 of the Code apply to remote-control, signaling, and power-limited circuits, except as amended by Article 725 for specified conditions. A remote-control, signaling, or power-limited circuit is the portion of the wiring system between the load side of the overcurrent device or the power-limited supply and all connected equipment. The circuit is categorized as Class 1, Class 2, or Class 3. Class 1 circuits are not permitted to exceed 600 volts. In many cases, Class 1 circuits are extensions of power systems and are subject to the requirements of the power systems, except under the following conditions: (1) Conductors sized 16 AWG and 18 AWG may be used if properly protected against overcurrent (see 725.23). (2) Where damage to the circuit would introduce a hazard, the circuit must be mechanically protected by a suitable means [see 725.8(B)]. (3) The adjustment factors of 310.15(B)(2) apply only if such conductors carry a continuous load (see 725.28 for the exact requirements for adjustment factors affecting ampacity). Class 1 remote-control circuits are commonly used to operate motor controllers in conjunction with moving equipment or mechanical processes, elevators, conveyors, and other such equipment. Class 1 remote-control circuits may also be used as shunt trip circuits for circuit breakers. Class 1 signaling circuits often operate at 120 volts but are not limited to this value. Conductors and equipment on the supply side of overcurrent protection, transformers, or current-limiting devices of Class 2 and Class 3 circuits must be installed according to the applicable requirements of Chapter 3. Load-side conductors and equipment must comply with Article 725. Class 2 and Class 3 conductors are required to be separated from, and not occupy, the same raceways, cable trays, cables, or enclosures as electric light, power, and Class 1 conductors. Exceptions are noted in 725.55. Dry-cell batteries are considered Class 2 power supplies, provided the voltage is 30 volts or less and the capacity is equal to or less than that available from series-connected No. 6 carbon-zinc cells. (A No. 6 dry-cell battery is cylindrically shaped with nominal dimensions of 2.5 in. in diameter by 6 in. tall and weighing just over 2 lb. A No. 6 dry-cell battery is about 10 times the volume of the standard D-cell battery commonly used in flashlights.) Circuits originating from thermocouples are classified Class 2 circuits also. Neither dry-cell batteries nor thermocouples are required to be listed.