I’m confident we’re both describing a thermal-magnetic circuit breaker. Many are different or have added functions but the most common are inverse time. The solenoid action you mentioned is what I’m referring to as the magnetic trip. There are curves and charts for how these two functions relate for any specific breaker so that coordinations can be made across a system.
I added the bit about ambient temperatures and bad connections becuase that added heat would cause the breaker to trip on thermal even though the actual current was under the rated current.
The nec addresses when, where and how they are used and when allowed or disallowed. The whys and why nots for one over another are shoehorned into the scene by anyone who cares to argue about it. Ussually engineers, inspectors and electricians, the last two tend to carry their own personal NFPA branded Dead Horse Whippin’-Sticks, but the electricians are better with them😁.