To me "Bayescraft" has the connotation of a particular mental attitude, one inspired by Eliezer Yudkowsky's fusion of the ev-psych, heuristics-and-biases literature with E.T. Jaynes' idiosyncratic take on "Bayesian probabilistic inference", and in particular the desiderata for an inference robot: take all relevant evidence into account, rather than filter evidence according to your ideological biases, and allow your judgement of a proposition's plausibility to move freely in the [0..1] range rather than seek all-or-nothing certainty in your belief.

Capitalized words are often technical terms. So "Traditional Rationality" refers to certain epistemic attitudes and methods which have, in the past, been called "rational" (a word which is several hundred years old). This frees up the lower-case word "rationality", which on this site is also a technical term.

Bayescraft is just a synonym for Rationallity, with connotations of a) Bayes theorem, since that's what epistemic rationallity must be based on, and b) the notion that rationallity is a skill which must be developed personally and as a group (see also: Martial art of Rationallity (oh look, more capitals!))

The capitals are just for emphasis of concepts that the writer thinks are fundamentally important.