The DNA in all the mitochondria in one person’s body is identical (except for occasional mutations), but the mitochondria themselves can be very different. Mitochondrial DNA has a pretty limited number of genes on it, and if I recall correctly, none of them code for entire, functioning proteins. They just code for polypeptide subunits that associate with other subunits coded for in the nuclear DNA to make functioning proteins. As far as I know, the polypeptides coded for in the mitochondrial DNA are all too big to be efficiently transported in from the cytoplasm, so they’re made in place. If it wasn’t for this, mitochondrial DNA would have disappeared long ago.
The proteins and polypeptides that enter from the cytoplasm are different in different cell types, so mitochondria can vary quite a bit from one cell type to another.
There are some mitochondrial disorders where a defect in the mitochonrial DNA causes problems in only one cell type because the subunits made in the mitochondria don’t mesh with the ones coded for by nuclear DNA in certain tissues, but work fine in others.