Ah, now, welcome to my pet zone.
This is one thing I've spent many years studying (being a science communicator, definition is kind of an occupational hazard).
Remirol kind of hits the nail on the head. There are several interpreted meanings to the term, depending on the community you're communicating with.
You're correct that 'doubt' lies at the core of all meanings of the term. Yet the placement of this doubt depends on the context of the term. Most people in the community tend to associate the word 'skeptic' with an opposition to an otherwise accepted belief. In other words, it's always a negative thing that conflicts with a perceived truth. Take 'climate change skeptic' for an example.
Yet in communities such as this one, to be a skeptic is associated not with any one particular stance or context, but rather with an overall philosophy.
This contrast makes it difficult to communicate the core goals of critical thinking. People will readily associate the word skeptic with an adopted position before they will with an epistemology. Personally, even though I share this philosophy, in my line of work I avoid nominating myself as a skeptic, for this very reason.
Athon