Kelly B. answered 07/30/19
Caring tutor who wants to see all children succeed!
In this case, they are not the same thing.
'To commiserate' means you share someone's grief ( a noun form is rare).
'Condolences' means you feel bad for someone ( verb form is rare).
If you needed more clarity,
in general we don't say " we give our commiseration to you'. The more normal thing is to give or offer someone your condolences.