I dunno. Lots of guys build custom cars which are truly one-of-a-kind. Things are done in a way which no one else has done.

Some do it for a customer using a customer's ideas. Still, working within the customer's wishes, the builder must do what he does and compromises must sometimes be made. Many builders don't want to and will not do certain things. After all, his name is on the car. Some build custom cars with no buyer in mind and soon find an ass which fits the seat perfectly. I deem either a custom if it is truly unique.

As in razor makers, some build what they want and soon, someone will have to have it. As long as it is unique and not produced in numbers, I consider it a custom made razor. The maker built it as he saw fit and is proud of the outcome, current buyer or not. If truly a fine maker, someone will come along and just have to have it.

I suppose what some have commissioned turns out to be a monster with issues. Cars or Razors.
A great maker will not be concerned with a customer's weird desires as much as what his name goes on.

I have a Charlie Lewis razor. I did not commission it, nor have any input on it's features. But when I saw it, I wanted it.
I know there may be some he has/will make which may be close, but not quite the same.
I definitely consider it a custom razor. JMO