I think maybe done by hand? The S doesn't match either Sackers or Engravers, and other characters fail to match Trade Gothic Extended, which was my other guess. It's not Burin Sans either. I'm out of options. It's very nice.

Custom, certainly. Closest fonts I know are Frieze and Sassoon Dotted, but these don’t have the rigid structure of the Care logo. If you want a similar look, I’d follow the midline of a linear serif with dots.