At same time Champion & Druid have both - Class DC and Spell DC.
Please note that they are usually wrote as "<class name> class DC" and "spell attack" and "spell DC".
The classes mainly gives you training in "<class name> class DC" and increases when advancing. Rarely "hand" traits/actions/feats (T/A/F) on "* DC".
The multiclassing trains you in... newly taken "<class name> class DC".
This means that theoretically multiclassing Champion with Druid you would have:
- champion class DC
- divine spell attack
- divine spell DC
- druid class DC
- primal spell attack
- primal spell DC
Each of them tracked independently.
Usually T/A/F have origin of specific class and that's "class DC" should be used.
What if T/A/F is from non-class origin - ancestry, background, etc - AND refer to "class DC"?
I dunno if such case already exist. If so, then probably you have to choose highest "class DC" you are tracking in case of multiclassing.
EDIT:
Example of pure "class DC" is section "Critical Specialization Effects" for Brawling and Sling.