Consciousness/awareness/Bewusstsein only means, that one observes or is capable of observing. The reflexivity conveyed by self or selbst means, that one observes oneself or is capable of doing so. Generically self-conscious and selbstbewusst are perfectly synonymous.
The difference comes from what particularly one observes in oneself, or what the result of that observance should be. That is certainly determined by the philosophy or world view that motivates the observance in the first place.
If one observes oneself’s strengths in particular or the observance results in awareness of these strengths, then it may yield self-confidence/Selbstbewusstsein/Selbstvertrauen.
If one observes oneself’s weaknesses and imperfections in particular or the observance results in awareness of these weaknesses and imperfections, then it may yield self-consciousness (in casual meaning).
The German Selbstbewusstsein used to be associated with strengths. But it’s more and more associated with weaknesses (see: healthy living, ecological footprint).