I'm not familiar with California regulations but I am a former city planner and tax assessor.
My experience defines legal non-conforming uses as uses which are not in conformity with current zoning but are legal due to grandfathering or zoning variance.
My sense tells me the same thing as your hands-on experience. That's why I'd describe a use that requires a CUP but is defined within the ordinance as an allowable use, as a "legal, conforming" use.
And I guess that's my point (as I see it):
The zoning code describes a number of allowable uses.
Some are allowed by right; there is no additional process to use the property for those uses.
Some are allowed by conditional use permits; and those can be segmented into an "administrative review" or a "planning commission review". I don't want to characterize the administrative review as a mere formality, but as a rule, unless there is something specific about the property's location that would deem the use undesirable, they are routinely approved.
The planning commission use is more complex. An example of that occurred in my residential neighborhood a few years ago. A home was being used as a residential day care facility. This is permitted use, but it it limits the number of children at the facility. If the facility wants to have enroll more than that, it can apply for a conditional use. That conditional use requires planning commission approval.
Interestingly enough, in my example, the planning commission turned down the original request down. The owner of the home then had the right to have her case heard before the city council. The city council approved the use. It wasn't a zoning variance; it was an approved use (by code) but required the conditional use permit.
In that example, the CUP does not transfer with the property if sold.