All of these variants are expected to interoperate flawlessly, and they do.
Unfortunately, I have seen cases where some of these claimed USB-RS232 devices didn't work. While others did. So obviously the failing devices aren't meeting spec. Exactly why, I am not sure. Sometimes communication was ok with box X but not box Y. The answer was throw unreliable one away and get different one made by somebody else. Somewhere I have a list of "known good" manufacturer's. There is a lot of chatter about this on hobbyist sites.

Update: from Hardware specific problems

RS232 ports which are physically mounted in a computer are often powered by three power sources: +5 Volt for the UART logic, and -12 Volt and +12 Volt for the output drivers. USB however only provides a +5 Volt power source. Some USB to RS232 converters use integrated DC/DC converters to create the appropriate voltage levels for the RS232 signals, but in very cheap implementations, the +5 Volt voltage is directly used to drive the output. This may sound strange, but many RS232 ports recognize a voltage above 2 Volt as a space signal, where a voltage of 0 Volt or less is recognized as a mark signal. This is not according to the original standard, because in the original RS232 standard, all voltages between -3 Volt and +3 Volt result in an undefined signal state. The well known Maxim MAX232 series of RS232 driver chips have this non-standard behavior for example. Although the outputs of these drivers swings between -10 Volt and +10 Volt, the inputs recognize all signals swinging below 0 Volt and above 2 Volt as valid signals.

This non-standard behavior of RS232 inputs makes it even more difficult to select the right RS232 to USB converter. If you connect and test an RS232 to USB converter over a serial line with another device, it might work with some devices, but not with others. This can particularly become a problem with industrial applications. Low-cost computers are often equipped with cheap RS232 drivers and when you test the RS232 to USB converter with such a computer, it might work. But the same converter may fail if you try it in an industrial environment. The chances that RS232 ports from low-cost computers accept signals in the 0..5 Volt range are higher than with industrial equipment which is often specifically designed to be immune for noise.