Non-consensual tow
A tow you did not request — police-ordered or from private property. It is the only category whose price a state or city may regulate.
In practice
This is the hinge concept for the whole of towing law. Under 49 U.S.C. § 14501(c)(1) federal law preempts state and local regulation of carrier prices — but § 14501(c)(2)(C) carves out non-consensual tows, letting states and cities cap what you are charged for a removal you never asked for.
The practical test is not who benefited from the tow but whether you chose it. A police-ordered removal after a collision and a trespass tow from a parking lot are both non-consensual: you could not shop the price, negotiate the terms, or decline. A tow you telephoned for after a breakdown is consensual and generally unregulated, however expensive it turns out to be. Establishing which category applies is the first step in any dispute, because it decides whether there is a cap to point at.