Just because a device has a DE-9 connector, it may have nothing to do with RS-232 standard.
The RS-232 standard allows only two connectors, and DE-9 is not one of them.
So strictly speaking, and technically, all RS-232 interfaces with DE-9 connector or any other connector than the allowed connectors are custom/proprietary implementations.
That said, when IBM made the dual RS-232 interface card for the IBM 5170 (the PC/AT might be more familiar term), one of the ports had to use a smaller connector to fit into card slot, so this custom implementation developed and became a de facto standard.
And even if it does have a custom connector, if it still implements RS-232 interface electrically but with a non-standard physical connector, be it DE-9 or 8P8C modular jack or 3.5mm TRS connector, in a pinch and in common language it can still be called an RS-232 port. After all, it only takes an adapter or a cable to end up with a standard connector.
And even more technically, RS-232 devices may still be incompatible - the standard does not define a protocol, only an electrical interface for binary data. While you may safely assume that asynchronous start-stop framing protocol with NRZ line coding is used as an UART is very common, it's not defined by standard. You could use any binary data encoding like Morse code, FM, Manchester or EFM if you wanted, and it will technically still be an RS-232 interface, but it would seriously limit the ability to communicate with other equipment due to bit protocol and line code.
So again, the de facto protocol is just made with UARTs, but not mandated by the RS-232 standard.