Well no.
The distinction is digital and music, which relates to different routines on software side.
So usually you have a routine that plays music in background and another routine that plays digital sound effects.
Wether this is really a digital device or analog synth playing in the end depends on the hardware choice.
For older games it usually is
SB for digital and OPL for music, where OPL has a analog output. On a typical SB card this on the same hardware board.
If you look at newer boards you usually have SB for digital effects and MIDI music played through a Wavetable Synthesizer, that is also digital.
Often on a soundcard several components were put on the same board.
f.e. on a SB you got a so called Codec chip that can play digital samples and independent a OPL FM-Synthesizer with analog output.
The Codec output goes to a digital to analog converter and then there is a digital controlled mixer chip that allows to set the volumes of the analog inputs. They are mixed together to one analog output.
Now this concept was extended, so for example on a EWS64 you have a Codec chip that has digital,OPL and mixer capabilities already included and in addition there is a wavetable synthesizer that puts out a analog audio signal. Now the signal can be routed, f.e. from the Codec Chip to the wavetable synthesizer chip or the other way around. Just as example you could imagine plugging in an external audio source, route this to the wavetable synthesizer that is also capable of applying additional digital effects as chorus and reverb. The the signal is routed to the codec chip where in the mixer part digital sound effects are added and goes then to the analog output of the card.
On older cards the signal routing is fixed, on newer cards this can sometimes be configured.