Most DACs convert both PCM and DSD to a intermediate format, something like 5 bit PCM at a high sample rate and noise shaped. That isn’t PCM and it isn’t DSD. There’s a continuum of intermediate formats that can work. It’s much easier to build a 5 bit DAC than a 20 bit DAC. Then you can low pass filter the high rate analog signal to trim off the noise. There are complications if you have to do it in a single chip, but that’s for another time.
R-2R DACs can only deal with PCM so they have to convert DSD to PCM to play it (all that requires is a digital low pass filter.)
One bit DACs can only deal with DSD so they need to convert PCM to DSD. Ladder DACs and one bit DACs aren’t exactly typical.