It's a Latin medical term for "caused by or characteristic of old age". It wasn't derogatory when a lot of people knew Latin, but has become so in general use.

Yup, I got it, but people also thought dementia was unavoidable for seniors. Quoting Wikipedia: Dementia in the elderly was once called senile dementia or senility, and viewed as a normal and somewhat inevitable aspect of aging. en.m.wikipedia.org/wiki/Dementi...

I am not interested in terminological subtleties for their own sake. I am interested in the question whether the processes leading to the purple color and failing brain are related according to any research, or they are two independent processes separately correlated with aging

Purpura is due to minor blood vessels leaking under the skin. Fronto-temporal dementia, which is what Trump has, is thought to be a group of conditions with different causes. (Most dementia research is on Alzheimer's syndrome because it's more common.) So the short answer is "we can't rule it out".

Thanks!